// Numbas version: finer_feedback_settings
{"name": "Equations du second degr\u00e9 : 01 - R\u00e9solution \u00e0 l'aide des formules.", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Equations du second degr\u00e9 : 01 - R\u00e9solution \u00e0 l'aide des formules.", "tags": [], "metadata": {"description": "<p>R&eacute;soudre des &eacute;quations du second degr&eacute; &agrave; une inconnue (cas d'un discriminant &gt; 0, deux racines enti&egrave;res r&eacute;elles et discr&egrave;tes) &agrave; l'aide des formules.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p style=\"background-color: aqua; text-align: center;\"><span class=\"\" style=\"color: #0000ff;\"><strong>M&eacute;thode g&eacute;n&eacute;rale de r&eacute;solution des &eacute;quations du second degr&eacute;<br/></strong></span></p>\n<p><br/>Soit l'&eacute;quation du second degr&eacute; : \\(\\color{red}{a x^{2} + b x + c = 0}\\) (a, b et c \\(\\in \\mathbb{R}\\), a \\(\\neq\\) 0).</p>\n<p>Son discriminant ($\\Delta$ = delta) est : $\\color{red}{\\Delta=b^{2}-4 a c}$</p>\n<ul>\n<li>Si $\\Delta&gt;0$ : L'&eacute;quation admet deux solutions distinctes $\\rightarrow S=\\left\\{x_{1} ; x_{2}\\right\\}$.<br/>$$<br/>\\color{red}{x_{1}=\\frac{-b-\\sqrt{\\Delta}}{2 a}}~~\\text { et }~~\\color{red}{x_{2}=\\frac{-b+\\sqrt{\\Delta}}{2 a}} \\rightarrow \\text { Forme factoris&eacute;e }: a\\left(x-x_{1}\\right)\\left(x-x_{2}\\right)=0<br/>$$</li>\n</ul>\n<p style=\"text-align: center;\"><span style=\"text-decoration: underline;\"><em>Nota :</em></span> On les appelles parfois formules de Shreedhara Acharya (math&eacute;maticien indien du X$^{\\text {&egrave;me }}$si&egrave;cle).</p>\n<ul>\n<li>Si $\\Delta=0$ : L'&eacute;quation admet une unique solution $\\rightarrow S=\\left\\{x_{0}\\right\\}$.<br/>$$<br/>\\color{red}{x_{0}=\\frac{-b}{2 a}} \\rightarrow \\text { Forme factoris&eacute;e }: a\\left(x-x_{0}\\right)^{2}=0<br/>$$</li>\n<li>Si $\\Delta&lt;0$ : L'&eacute;quation n'a pas de solution r&eacute;elle $\\rightarrow S=\\varnothing$.</li>\n</ul>", "advice": "<p>On nous demande de trouver les racines de diverses &eacute;quations du second degr&eacute; en utilisant les formules. Pour nous permettre de le faire, on nous demande &agrave; chaque fois de commencer par identifier les coefficients \\( a \\), \\( b \\) et \\( c \\).</p>\n<p></p>\n<p>a)</p>\n<p>\\( \\simplify{ {a1}x^2 + {b1}x + {c1} } =0 \\)</p>\n<p>Les coefficients de cette &eacute;quation peuvent &ecirc;tre simplement lus &agrave; partir de l'&eacute;quation, en prenant soin de tenir compte des valeurs positives et n&eacute;gatives :</p>\n<p>\\( a = \\)&nbsp; \\( \\var{a1}\\) &nbsp;&nbsp;&nbsp; \\( b = \\)&nbsp; \\( \\var{b1}\\) &nbsp; et&nbsp; \\( c = \\)&nbsp; \\( \\var{c1}\\)</p>\n<ul>\n<li>Nous pla&ccedil;ons ces valeurs dans la formule du discriminant en prenant soin de mettre des parenth&egrave;ses au moins autour de celles qui sont n&eacute;gatives :</li>\n</ul>\n<p style=\"text-align: center;\">$\\color{red}{\\Delta=b^{2}-4 a c}$ &nbsp;&nbsp;&nbsp; devient &nbsp;&nbsp;&nbsp; $\\Delta=(\\var{b1})^2 -4 \\times (\\var{a1}) \\times (\\var{c1}) = \\var{d1}$</p>\n<ul>\n<li>Nous pla&ccedil;ons $\\Delta$, a et b dans les formules des racines en prenant soin de mettre des parenth&egrave;ses au moins autour de celles qui sont n&eacute;gatives :</li>\n</ul>\n<p style=\"text-align: center;\">$\\color{red}{x_{1}=\\frac{-b-\\sqrt{\\Delta}}{2 a}}$ &nbsp;&nbsp;&nbsp; devient &nbsp;&nbsp;&nbsp; $x_{1}=\\frac{-(\\var{b1}) - \\sqrt{\\var{d1}}}{2 \\times (\\var{a1})}=\\var{x1}$</p>\n<p style=\"text-align: center;\">$\\color{red}{x_{2}=\\frac{-b+\\sqrt{\\Delta}}{2 a}}$ &nbsp;&nbsp;&nbsp; devient &nbsp;&nbsp;&nbsp; $x_{2}=\\frac{-(\\var{b1}) + \\sqrt{\\var{d1}}}{2 \\times (\\var{a1})}=\\var{x2}$</p>\n<p></p>\n<p>b)</p>\n<p>\\( \\simplify{ {a2}x^2 + {b2}x + {c2} } =0 \\)</p>\n<p>Les coefficients de cette &eacute;quation peuvent &ecirc;tre simplement lus &agrave; partir de l'&eacute;quation, en prenant soin de tenir compte des valeurs positives et n&eacute;gatives :</p>\n<p>\\( a = \\)&nbsp; \\( \\var{a2}\\) &nbsp; &nbsp; \\( b = \\)&nbsp; \\( \\var{b2}\\) &nbsp; et&nbsp; \\( c = \\)&nbsp; \\( \\var{c2}\\)</p>\n<ul>\n<li>Nous pla&ccedil;ons ces valeurs dans la formule du discriminant en prenant soin de mettre des parenth&egrave;ses au moins autour de celles qui sont n&eacute;gatives :</li>\n</ul>\n<p style=\"text-align: center;\">$\\color{red}{\\Delta=b^{2}-4 a c}$ &nbsp;&nbsp;&nbsp; devient &nbsp;&nbsp;&nbsp; $\\Delta=(\\var{b2})^2 -4 \\times (\\var{a2}) \\times (\\var{c2}) = \\var{d2}$</p>\n<ul>\n<li>Nous pla&ccedil;ons $\\Delta$, a et b dans les formules des racines en prenant soin de mettre des parenth&egrave;ses au moins autour de celles qui sont n&eacute;gatives :</li>\n</ul>\n<p style=\"text-align: center;\">$\\color{red}{x_{1}=\\frac{-b-\\sqrt{\\Delta}}{2 a}}$ &nbsp;&nbsp;&nbsp; devient &nbsp;&nbsp;&nbsp; $x_{1}=\\frac{-(\\var{b2}) - \\sqrt{\\var{d2}}}{2 \\times (\\var{a2})}=\\var{y1}$</p>\n<p style=\"text-align: center;\">$\\color{red}{x_{2}=\\frac{-b+\\sqrt{\\Delta}}{2 a}}$ &nbsp;&nbsp;&nbsp; devient &nbsp;&nbsp;&nbsp; $x_{2}=\\frac{-(\\var{b2}) + \\sqrt{\\var{d2}}}{2 \\times (\\var{a2})}=\\var{y2}$</p>\n<p></p>\n<p>c)</p>\n<p>\\( \\simplify{ {a3}x^2 + {b3}x + {c3} } =0 \\)</p>\n<p>Les coefficients de cette &eacute;quation peuvent &ecirc;tre simplement lus &agrave; partir de l'&eacute;quation, en prenant soin de tenir compte des valeurs positives et n&eacute;gatives :</p>\n<p>\\( a = \\)&nbsp; \\( \\var{a3}\\) &nbsp; &nbsp; \\( b = \\)&nbsp; \\( \\var{b3}\\) &nbsp; et&nbsp; \\( c = \\)&nbsp; \\( \\var{c3}\\)</p>\n<ul>\n<li>Nous pla&ccedil;ons ces valeurs dans la formule du discriminant en prenant soin de mettre des parenth&egrave;ses au moins autour de celles qui sont n&eacute;gatives :</li>\n</ul>\n<p style=\"text-align: center;\">$\\color{red}{\\Delta=b^{2}-4 a c}$ &nbsp;&nbsp;&nbsp; devient &nbsp;&nbsp;&nbsp; $\\Delta=(\\var{b3})^2 -4 \\times (\\var{a3}) \\times (\\var{c3}) = \\var{d3}$</p>\n<ul>\n<li>Nous pla&ccedil;ons $\\Delta$, a et b dans les formules des racines en prenant soin de mettre des parenth&egrave;ses au moins autour de celles qui sont n&eacute;gatives :</li>\n</ul>\n<p style=\"text-align: center;\">$\\color{red}{x_{1}=\\frac{-b-\\sqrt{\\Delta}}{2 a}}$ &nbsp;&nbsp;&nbsp; devient &nbsp;&nbsp;&nbsp; $x_{1}=\\frac{-(\\var{b3}) - \\sqrt{\\var{d3}}}{2 \\times (\\var{a3})}=\\var{z1}$</p>\n<p style=\"text-align: center;\">$\\color{red}{x_{2}=\\frac{-b+\\sqrt{\\Delta}}{2 a}}$ &nbsp;&nbsp;&nbsp; devient &nbsp;&nbsp;&nbsp; $x_{2}=\\frac{-(\\var{b3}) + \\sqrt{\\var{d3}}}{2 \\times (\\var{a3})}=\\var{z2}$</p>\n<p></p>\n<p></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a1": {"name": "a1", "group": "Question A", "definition": "random(2..9)", "description": "", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "Question A", "definition": "random(-9..9 except 0 except 1 except {a1})", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Question A", "definition": "random(-9..9 except 0 except 1 except {a1} except {x1})", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Question A", "definition": "-{a1}*({x1}+{x2})", "description": "", "templateType": "anything", "can_override": false}, "c1": {"name": "c1", "group": "Question A", "definition": "{a1}*{x1}*{x2}", "description": "", "templateType": "anything", "can_override": false}, "plus": {"name": "plus", "group": "Trial check", "definition": "(-{b1}+sqrt({b1}^2-4*{a1}*{c1}))/(2*{a1})", "description": "", "templateType": "anything", "can_override": false}, "minus": {"name": "minus", "group": "Trial check", "definition": "(-{b1}-sqrt({b1}^2-4*{a1}*{c1}))/(2*{a1})", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Question B", "definition": "random(2..9 except {a1})", "description": "", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "Question B", "definition": "random(-9..9 except 0 except 1 except {a2})", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Question B", "definition": "random(-9..9 except 0 except 1 except {a2} except {y1})", "description": "", "templateType": "anything", "can_override": false}, "b2": {"name": "b2", "group": "Question B", "definition": "-{a2}*({y1}+{y2})", "description": "", "templateType": "anything", "can_override": false}, "c2": {"name": "c2", "group": "Question B", "definition": "{a2}*{y1}*{y2}", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "Question C", "definition": "random(2..9 except {a1} except {a2})", "description": "", "templateType": "anything", "can_override": false}, "z1": {"name": "z1", "group": "Question C", "definition": "random(-9..9 except 0 except 1 except {a3})", "description": "", "templateType": "anything", "can_override": false}, "z2": {"name": "z2", "group": "Question C", "definition": "random(-9..9 except 0 except 1 except {a3} except {z1})", "description": "", "templateType": "anything", "can_override": false}, "b3": {"name": "b3", "group": "Question C", "definition": "-{a3}*({z1}+{z2})", "description": "", "templateType": "anything", "can_override": false}, "c3": {"name": "c3", "group": "Question C", "definition": "{a3}*{z1}*{z2}", "description": "", "templateType": "anything", "can_override": false}, "d1": {"name": "d1", "group": "Question A", "definition": "{b1}^2-4*{a1}*{c1}", "description": "", "templateType": "anything", "can_override": false}, "d2": {"name": "d2", "group": "Question B", "definition": "{b2}^2-4*{a2}*{c2}", "description": "", "templateType": "anything", "can_override": false}, "d3": {"name": "d3", "group": "Question C", "definition": "{b3}^2-4*{a3}*{c3}", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [{"name": "Trial check", "variables": ["minus", "plus"]}, {"name": "Question A", "variables": ["x1", "x2", "a1", "b1", "c1", "d1"]}, {"name": "Question B", "variables": ["y1", "y2", "a2", "b2", "c2", "d2"]}, {"name": "Question C", "variables": ["z1", "z2", "a3", "b3", "c3", "d3"]}, {"name": "Unnamed group", "variables": []}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Pour les &eacute;quations suivantes, identifiez d'abord les coefficients, puis utilisez les formules pour calculer les racines :</p>"}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>\\( \\simplify{ {a1}x^2 + {b1}x + {c1} } =0 \\)</p>\n<p><span class=\"VIiyi\" jsaction=\"mouseup:BR6jm\" jsname=\"jqKxS\" lang=\"fr\"><span jsaction=\"agoMJf:PFBcW;usxOmf:aWLT7;jhKsnd:P7O7bd,F8DmGf;Q4AGo:Gm7gYd,qAKMYb;uFUCPb:pvnm0e,pfE8Hb,PFBcW;f56efd:dJXsye;EnoYf:KNzws,ZJsZZ,JgVSJc;zdMJQc:cCQNKb,ZJsZZ,zchEXc;Ytrrj:JJDvdc;tNR8yc:GeFvjb;oFN6Ye:hij5Wb;bmeZHc:iURhpf;Oxj3Xe:qAKMYb,yaf12d\" jsname=\"txFAF\" class=\"JLqJ4b ChMk0b\" data-language-for-alternatives=\"fr\" data-language-to-translate-into=\"en\" data-phrase-index=\"2\" data-number-of-phrases=\"3\" jscontroller=\"Zl5N8\" jsdata=\"uqLsIf;_;$118\" jsmodel=\"SsMkhd\"><span jsaction=\"click:qtZ4nf,GFf3ac,tMZCfe; contextmenu:Nqw7Te,QP7LD; mouseout:Nqw7Te; mouseover:qtZ4nf,c2aHje\" jsname=\"W297wb\">Les coefficients de cette &eacute;quation sont :</span></span></span></p>\n<p>\\( a = \\)&nbsp; [[0]] &nbsp; \\( b = \\)&nbsp; [[1]] &nbsp; et&nbsp; \\( c = \\)&nbsp; [[2]]</p>\n<p>Utilisez la formule pour trouver le discriminant : $\\Delta=$ [[5]]</p>\n<p><span class=\"VIiyi\" jsaction=\"mouseup:BR6jm\" jsname=\"jqKxS\" lang=\"fr\"><span jsaction=\"agoMJf:PFBcW;usxOmf:aWLT7;jhKsnd:P7O7bd,F8DmGf;Q4AGo:Gm7gYd,qAKMYb;uFUCPb:pvnm0e,pfE8Hb,PFBcW;f56efd:dJXsye;EnoYf:KNzws,ZJsZZ,JgVSJc;zdMJQc:cCQNKb,ZJsZZ,zchEXc;Ytrrj:JJDvdc;tNR8yc:GeFvjb;oFN6Ye:hij5Wb;bmeZHc:iURhpf;Oxj3Xe:qAKMYb,yaf12d\" jsname=\"txFAF\" class=\"JLqJ4b ChMk0b\" data-language-for-alternatives=\"fr\" data-language-to-translate-into=\"en\" data-phrase-index=\"4\" data-number-of-phrases=\"5\" jscontroller=\"Zl5N8\" jsdata=\"uqLsIf;_;$154\" jsmodel=\"SsMkhd\"><span jsaction=\"click:qtZ4nf,GFf3ac,tMZCfe; contextmenu:Nqw7Te,QP7LD; mouseout:Nqw7Te; mouseover:qtZ4nf,c2aHje\" jsname=\"W297wb\">Utilisez maintenant les formules pour trouver les racines :</span></span></span></p>\n<p>\\( x_1 = \\)&nbsp; [[3]]</p>\n<p>\\( x_2 = \\)&nbsp; [[4]]</p>\n<p><sup><span class=\"prompt content-area\" localise-data-jme-context-description=\"part.prompt\"><em>(<span class=\"VIiyi\" jsaction=\"mouseup:BR6jm\" jsname=\"jqKxS\" lang=\"fr\"><span jsaction=\"agoMJf:PFBcW;usxOmf:aWLT7;jhKsnd:P7O7bd,F8DmGf;Q4AGo:Gm7gYd,qAKMYb;uFUCPb:pvnm0e,pfE8Hb,PFBcW;f56efd:dJXsye;EnoYf:KNzws,ZJsZZ,JgVSJc;zdMJQc:cCQNKb,ZJsZZ,zchEXc;Ytrrj:JJDvdc;tNR8yc:GeFvjb;oFN6Ye:hij5Wb;bmeZHc:iURhpf;Oxj3Xe:qAKMYb,yaf12d\" jsname=\"txFAF\" class=\"JLqJ4b ChMk0b\" data-language-for-alternatives=\"fr\" data-language-to-translate-into=\"en\" data-phrase-index=\"6\" data-number-of-phrases=\"7\" jscontroller=\"Zl5N8\" jsdata=\"uqLsIf;_;$193\" jsmodel=\"SsMkhd\"><span jsaction=\"click:qtZ4nf,GFf3ac,tMZCfe; contextmenu:Nqw7Te,QP7LD; mouseout:Nqw7Te; mouseover:qtZ4nf,c2aHje\" jsname=\"W297wb\">Si vous &ecirc;tes s&ucirc;r que vos racines sont correctes mais qu'elles sont mal marqu&eacute;es, inversez-les</span></span></span>).</em></span></sup></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a1}", "maxValue": "{a1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b1}", "maxValue": "{b1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{c1}", "maxValue": "{c1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x1}", "maxValue": "{x1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x2}", "maxValue": "{x2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{d1}", "maxValue": "{d1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>\\( \\simplify{ {a2}x^2 + {b2}x + {c2} } =0 \\)</p>\n<p><span class=\"VIiyi\" jsaction=\"mouseup:BR6jm\" jsname=\"jqKxS\" lang=\"fr\"><span jsaction=\"agoMJf:PFBcW;usxOmf:aWLT7;jhKsnd:P7O7bd,F8DmGf;Q4AGo:Gm7gYd,qAKMYb;uFUCPb:pvnm0e,pfE8Hb,PFBcW;f56efd:dJXsye;EnoYf:KNzws,ZJsZZ,JgVSJc;zdMJQc:cCQNKb,ZJsZZ,zchEXc;Ytrrj:JJDvdc;tNR8yc:GeFvjb;oFN6Ye:hij5Wb;bmeZHc:iURhpf;Oxj3Xe:qAKMYb,yaf12d\" jsname=\"txFAF\" class=\"JLqJ4b ChMk0b\" data-language-for-alternatives=\"fr\" data-language-to-translate-into=\"en\" data-phrase-index=\"2\" data-number-of-phrases=\"7\" jscontroller=\"Zl5N8\" jsdata=\"uqLsIf;_;$189\" jsmodel=\"SsMkhd\"><span jsaction=\"click:qtZ4nf,GFf3ac,tMZCfe; contextmenu:Nqw7Te,QP7LD; mouseout:Nqw7Te; mouseover:qtZ4nf,c2aHje\" jsname=\"W297wb\">Les coefficients de cette &eacute;quation sont :</span></span></span></p>\n<p>\\( a = \\)&nbsp; [[0]] &nbsp; \\( b = \\)&nbsp; [[1]] &nbsp; et&nbsp; \\( c = \\)&nbsp; [[2]]</p>\n<p>Utilisez la formule pour trouver le discriminant : $\\Delta=$ [[5]]</p>\n<p><span class=\"VIiyi\" jsaction=\"mouseup:BR6jm\" jsname=\"jqKxS\" lang=\"fr\"><span jsaction=\"agoMJf:PFBcW;usxOmf:aWLT7;jhKsnd:P7O7bd,F8DmGf;Q4AGo:Gm7gYd,qAKMYb;uFUCPb:pvnm0e,pfE8Hb,PFBcW;f56efd:dJXsye;EnoYf:KNzws,ZJsZZ,JgVSJc;zdMJQc:cCQNKb,ZJsZZ,zchEXc;Ytrrj:JJDvdc;tNR8yc:GeFvjb;oFN6Ye:hij5Wb;bmeZHc:iURhpf;Oxj3Xe:qAKMYb,yaf12d\" jsname=\"txFAF\" class=\"JLqJ4b ChMk0b\" data-language-for-alternatives=\"fr\" data-language-to-translate-into=\"en\" data-phrase-index=\"4\" data-number-of-phrases=\"7\" jscontroller=\"Zl5N8\" jsdata=\"uqLsIf;_;$191\" jsmodel=\"SsMkhd\"><span jsaction=\"click:qtZ4nf,GFf3ac,tMZCfe; contextmenu:Nqw7Te,QP7LD; mouseout:Nqw7Te; mouseover:qtZ4nf,c2aHje\" jsname=\"W297wb\">Utilisez maintenant les formules pour trouver les racines :</span></span></span></p>\n<p>\\( x_1 = \\)&nbsp; [[3]]</p>\n<p>\\( x_2 = \\)&nbsp; [[4]]</p>\n<p><sup><span class=\"prompt content-area\" localise-data-jme-context-description=\"part.prompt\"><em>(<span class=\"VIiyi\" jsaction=\"mouseup:BR6jm\" jsname=\"jqKxS\" lang=\"fr\"><span jsaction=\"agoMJf:PFBcW;usxOmf:aWLT7;jhKsnd:P7O7bd,F8DmGf;Q4AGo:Gm7gYd,qAKMYb;uFUCPb:pvnm0e,pfE8Hb,PFBcW;f56efd:dJXsye;EnoYf:KNzws,ZJsZZ,JgVSJc;zdMJQc:cCQNKb,ZJsZZ,zchEXc;Ytrrj:JJDvdc;tNR8yc:GeFvjb;oFN6Ye:hij5Wb;bmeZHc:iURhpf;Oxj3Xe:qAKMYb,yaf12d\" jsname=\"txFAF\" class=\"JLqJ4b ChMk0b\" data-language-for-alternatives=\"fr\" data-language-to-translate-into=\"en\" data-phrase-index=\"6\" data-number-of-phrases=\"7\" jscontroller=\"Zl5N8\" jsdata=\"uqLsIf;_;$193\" jsmodel=\"SsMkhd\"><span jsaction=\"click:qtZ4nf,GFf3ac,tMZCfe; contextmenu:Nqw7Te,QP7LD; mouseout:Nqw7Te; mouseover:qtZ4nf,c2aHje\" jsname=\"W297wb\">Si vous &ecirc;tes s&ucirc;r que vos racines sont correctes mais qu'elles sont mal marqu&eacute;es, inversez-les</span></span></span>).</em></span></sup></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a2}", "maxValue": "{a2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b2}", "maxValue": "{b2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{c2}", "maxValue": "{c2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{y1}", "maxValue": "{y1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{y2}", "maxValue": "{y2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{d2}", "maxValue": "{d2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>\\( \\simplify{ {a3}x^2 + {b3}x + {c3} } =0 \\)</p>\n<p><span class=\"VIiyi\" jsaction=\"mouseup:BR6jm\" jsname=\"jqKxS\" lang=\"fr\"><span jsaction=\"agoMJf:PFBcW;usxOmf:aWLT7;jhKsnd:P7O7bd,F8DmGf;Q4AGo:Gm7gYd,qAKMYb;uFUCPb:pvnm0e,pfE8Hb,PFBcW;f56efd:dJXsye;EnoYf:KNzws,ZJsZZ,JgVSJc;zdMJQc:cCQNKb,ZJsZZ,zchEXc;Ytrrj:JJDvdc;tNR8yc:GeFvjb;oFN6Ye:hij5Wb;bmeZHc:iURhpf;Oxj3Xe:qAKMYb,yaf12d\" jsname=\"txFAF\" class=\"JLqJ4b ChMk0b\" data-language-for-alternatives=\"fr\" data-language-to-translate-into=\"en\" data-phrase-index=\"2\" data-number-of-phrases=\"7\" jscontroller=\"Zl5N8\" jsdata=\"uqLsIf;_;$189\" jsmodel=\"SsMkhd\"><span jsaction=\"click:qtZ4nf,GFf3ac,tMZCfe; contextmenu:Nqw7Te,QP7LD; mouseout:Nqw7Te; mouseover:qtZ4nf,c2aHje\" jsname=\"W297wb\">Les coefficients de cette &eacute;quation sont :</span></span></span></p>\n<p>\\( a = \\)&nbsp; [[0]] &nbsp; \\( b = \\)&nbsp; [[1]]&nbsp; et&nbsp; \\( c = \\)&nbsp; [[2]]</p>\n<p>Utilisez la formule pour trouver le discriminant : $\\Delta=$ [[5]]</p>\n<p><span class=\"VIiyi\" jsaction=\"mouseup:BR6jm\" jsname=\"jqKxS\" lang=\"fr\"><span jsaction=\"agoMJf:PFBcW;usxOmf:aWLT7;jhKsnd:P7O7bd,F8DmGf;Q4AGo:Gm7gYd,qAKMYb;uFUCPb:pvnm0e,pfE8Hb,PFBcW;f56efd:dJXsye;EnoYf:KNzws,ZJsZZ,JgVSJc;zdMJQc:cCQNKb,ZJsZZ,zchEXc;Ytrrj:JJDvdc;tNR8yc:GeFvjb;oFN6Ye:hij5Wb;bmeZHc:iURhpf;Oxj3Xe:qAKMYb,yaf12d\" jsname=\"txFAF\" class=\"JLqJ4b ChMk0b\" data-language-for-alternatives=\"fr\" data-language-to-translate-into=\"en\" data-phrase-index=\"4\" data-number-of-phrases=\"7\" jscontroller=\"Zl5N8\" jsdata=\"uqLsIf;_;$191\" jsmodel=\"SsMkhd\"><span jsaction=\"click:qtZ4nf,GFf3ac,tMZCfe; contextmenu:Nqw7Te,QP7LD; mouseout:Nqw7Te; mouseover:qtZ4nf,c2aHje\" jsname=\"W297wb\">Utilisez maintenant les formules pour trouver les racines :</span></span></span></p>\n<p>\\( x_1 = \\)&nbsp; [[3]]</p>\n<p>\\( x_2 = \\)&nbsp; [[4]]</p>\n<p><sup><span class=\"prompt content-area\" localise-data-jme-context-description=\"part.prompt\"><em>(<span class=\"VIiyi\" jsaction=\"mouseup:BR6jm\" jsname=\"jqKxS\" lang=\"fr\"><span jsaction=\"agoMJf:PFBcW;usxOmf:aWLT7;jhKsnd:P7O7bd,F8DmGf;Q4AGo:Gm7gYd,qAKMYb;uFUCPb:pvnm0e,pfE8Hb,PFBcW;f56efd:dJXsye;EnoYf:KNzws,ZJsZZ,JgVSJc;zdMJQc:cCQNKb,ZJsZZ,zchEXc;Ytrrj:JJDvdc;tNR8yc:GeFvjb;oFN6Ye:hij5Wb;bmeZHc:iURhpf;Oxj3Xe:qAKMYb,yaf12d\" jsname=\"txFAF\" class=\"JLqJ4b ChMk0b\" data-language-for-alternatives=\"fr\" data-language-to-translate-into=\"en\" data-phrase-index=\"6\" data-number-of-phrases=\"7\" jscontroller=\"Zl5N8\" jsdata=\"uqLsIf;_;$193\" jsmodel=\"SsMkhd\"><span jsaction=\"click:qtZ4nf,GFf3ac,tMZCfe; contextmenu:Nqw7Te,QP7LD; mouseout:Nqw7Te; mouseover:qtZ4nf,c2aHje\" jsname=\"W297wb\">Si vous &ecirc;tes s&ucirc;r que vos racines sont correctes mais qu'elles sont mal marqu&eacute;es, inversez-les</span></span></span>).</em></span></sup></p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{a3}", "maxValue": "{a3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{b3}", "maxValue": "{b3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{c3}", "maxValue": "{c3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{z1}", "maxValue": "{z1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{z2}", "maxValue": "{z2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{d3}", "maxValue": "{d3}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "si-en", "si-fr", "plain-eu"], "correctAnswerStyle": "si-fr"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question", "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "STEPHAN GRIGNON", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14984/"}], "resources": []}]}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}, {"name": "STEPHAN GRIGNON", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/14984/"}]}