// Numbas version: exam_results_page_options
{"name": "ecuacion cuadratica 3", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"c": {"description": "", "templateType": "anything", "definition": "{a1}*{b1}*{c1}", "name": "c", "group": "Ungrouped variables"}, "b": {"description": "", "templateType": "anything", "definition": "{a1}*({b1}+{c1})", "name": "b", "group": "Ungrouped variables"}, "a1": {"description": "", "templateType": "randrange", "definition": "random(1..6#1)", "name": "a1", "group": "Ungrouped variables"}, "b1": {"description": "", "templateType": "randrange", "definition": "random(11..25#1)", "name": "b1", "group": "Ungrouped variables"}, "c1": {"description": "", "templateType": "randrange", "definition": "random(1..10#1)", "name": "c1", "group": "Ungrouped variables"}}, "ungrouped_variables": ["a1", "b1", "c1", "b", "c"], "preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": "1", "condition": ""}, "tags": [], "rulesets": {}, "functions": {}, "statement": "<p>La siguiente ecuaci&oacute;n puede ser convertida a una ecuaci&oacute;n cuadr&aacute;tica. Encuentre los valores de $x$ que satisfacen esta ecuaci&oacute;n.</p>\n<p style=\"padding-left: 30px;\">\\(\\var{a1}x+\\dfrac{\\simplify{{a1}*{b1}*{c1}}}{x}=\\simplify{{a1}*({b1}+{c1})}\\)</p>\n<p style=\"padding-left: 30px; text-align: left;\"></p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solving quadratic equations using a formula</p>"}, "name": "ecuacion cuadratica 3", "extensions": [], "advice": "<p>\\(\\var{a1}x+\\dfrac{\\simplify{{a1}*{b1}*{c1}}}{x}=\\simplify{{a1}*({b1}+{c1})}\\)</p>\n<p>Multiplicando cada t&eacute;rmino de la ecuaci&oacute;n por \\(x\\) obtenemos</p>\n<p>\\(\\var{a1}x^2+\\simplify{{a1}*{b1}*{c1}}=\\simplify{{a1}*({b1}+{c1})}x\\)</p>\n<p>Llevamos todos los t&eacute;rminos al lado izquierdo y los ordenamos de acuerdo a las potencias de \\(x\\) para obtener</p>\n<p>\\(\\var{a1}x^2-\\simplify{{a1}*({b1}+{c1})}x+\\simplify{{a1}*{b1}*{c1}}=0\\)</p>\n<p>La f&oacute;rmula para resolver una ecuaci&oacute;n cuadr&aacute;tica de la forma \\(ax^2+bx+c=0\\)&nbsp; est&aacute; dada por</p>\n<p style=\"padding-left: 30px;\">\\(x=\\dfrac{-b\\pm \\sqrt{b^2-4ac}}{2a}\\)</p>\n<p>En este ejemplo,&nbsp; \\(a=\\var{a1},\\,\\,\\,b=\\simplify{+-{a1}*({b1}+{c1})}\\)&nbsp; y \\(c=\\simplify{{a1}*{b1}*{c1}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(x=\\dfrac{\\var{b}\\pm \\sqrt{(-\\var{b})^2-4*\\var{a1}*\\var{c}}}{2*\\var{a1}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(x=\\dfrac{\\var{b}\\pm \\sqrt{\\simplify{{b}^2-4*{a1}*{c}}}}{\\simplify{2*{a1}}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(x=\\simplify{{b}+({b}^2-4*{a1}*{c})^0.5}/\\simplify{2*{a1}}=\\simplify{({b}+({b}^2-4*{a1}*{c})^0.5)/(2*{a1})}\\) &nbsp; &nbsp; &nbsp;&nbsp; o bien &nbsp; &nbsp; &nbsp;&nbsp; \\(x=\\simplify{{b}-({b}^2-4*{a1}*{c})^0.5}/\\simplify{2*{a1}}=\\simplify{({b}-({b}^2-4*{a1}*{c})^0.5)/(2*{a1})}\\)</p>\n<p style=\"padding-left: 60px;\"></p>\n<p></p>", "parts": [{"scripts": {}, "showFeedbackIcon": true, "prompt": "<p>Ingrese el mayor de los valores que satisfacen la ecuaci&oacute;n.&nbsp;</p>\n<p style=\"padding-left: 30px;\">\\(x = \\)&nbsp;[[0]]</p>\n<p>Ingrese el menor de los valores que satisfacen la ecuaci&oacute;n.&nbsp;</p>\n<p style=\"padding-left: 30px;\">\\(x = \\)&nbsp;[[1]]</p>", "marks": 0, "type": "gapfill", "gaps": [{"precision": "3", "scripts": {}, "mustBeReducedPC": 0, "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "minValue": "{b1}", "precisionMessage": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showPrecisionHint": false, "showFeedbackIcon": true, "strictPrecision": false, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain", "maxValue": "{b1}", "allowFractions": false, "mustBeReduced": false, "correctAnswerFraction": false}, {"precision": "3", "scripts": {}, "mustBeReducedPC": 0, "precisionType": "dp", "notationStyles": ["plain", "en", "si-en"], "precisionPartialCredit": 0, "minValue": "{c1}", "precisionMessage": "", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showPrecisionHint": false, "showFeedbackIcon": true, "strictPrecision": false, "marks": 1, "type": "numberentry", "correctAnswerStyle": "plain", "maxValue": "{c1}", "allowFractions": false, "mustBeReduced": false, "correctAnswerFraction": false}], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": []}], "variable_groups": [], "type": "question", "contributors": [{"name": "Ricardo Monge", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/471/"}]}]}], "contributors": [{"name": "Ricardo Monge", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/471/"}]}