// Numbas version: exam_results_page_options
{"name": "Solving quadratic equations 1(b)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"scripts": {}, "marks": 0, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "<p>Type in the greater of the two values that satisfies the equation. Input your answer correct to three decimal places.</p>\n<p style=\"text-align: left; padding-left: 30px;\">\\(x\\) =&nbsp;[[0]]</p>\n<p>Type in the lesser of the two values that satisfies the equation.&nbsp;Input your answer correct to three decimal places.</p>\n<p style=\"padding-left: 30px;\">\\(x\\) =&nbsp;[[1]]</p>", "type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "scripts": {}, "maxValue": "-{b1}/(2*{a1})+sqrt({b1}^2-4*{a1}*{c1})/(2*{a1})", "mustBeReduced": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "correctAnswerFraction": false, "allowFractions": false, "strictPrecision": false, "marks": 1, "variableReplacements": [], "precisionType": "dp", "showPrecisionHint": false, "minValue": "-{b1}/(2*{a1})+sqrt({b1}^2-4*{a1}*{c1})/(2*{a1})", "notationStyles": ["plain", "en", "si-en"], "precision": "3"}, {"precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "correctAnswerStyle": "plain", "scripts": {}, "maxValue": "-{b1}/(2*{a1})-sqrt({b1}^2-4*{a1}*{c1})/(2*{a1})", "mustBeReduced": false, "showFeedbackIcon": true, "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "correctAnswerFraction": false, "allowFractions": false, "strictPrecision": false, "marks": 1, "variableReplacements": [], "precisionType": "dp", "showPrecisionHint": false, "minValue": "-{b1}/(2*{a1})-sqrt({b1}^2-4*{a1}*{c1})/(2*{a1})", "notationStyles": ["plain", "en", "si-en"], "precision": "3"}]}], "statement": "<p>There are two values that satisfy the quadratic function below when&nbsp; \\(y=\\var{c1}\\):</p>\n<p style=\"padding-left: 30px;\">\\(y=\\var{a1}x^2+\\var{b1}x\\)</p>", "rulesets": {}, "variable_groups": [], "ungrouped_variables": ["a1", "b1", "c1"], "name": "Solving quadratic equations 1(b)", "functions": {}, "extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solving quadratic equations using a formula,</p>"}, "variablesTest": {"condition": "b1^2>4*a1*c1", "maxRuns": "1"}, "advice": "<p>The formula for solving a quadratic equation of the form &nbsp;\\(ax^2+bx+c=0\\) &nbsp;is given by</p>\n<p>\\(x=\\frac{-b\\pm \\sqrt{b^2-4ac}}{2a}\\)</p>\n<p>In this example &nbsp;\\(a=\\var{a1},\\,\\,\\,b=\\var{b1}\\) &nbsp;and &nbsp;\\(c=\\var{c1}\\)</p>\n<p style=\"padding-left: 60px;\">\\(x=\\frac{-\\var{b1}\\pm \\sqrt{\\var{b1}^2-4\\times\\var{a1}\\times\\var{c1}}}{2\\times\\var{a1}}\\)</p>\n<p style=\"padding-left: 60px;\">\\(x=\\frac{-\\var{b1}\\pm \\sqrt{\\simplify{{b1}^2-4*{a1}*{c1}}}}{\\simplify{2*{a1}}}\\)</p>\n<p style=\"padding-left: 60px;\">\\(x=\\simplify{(-{b1}+ ({b1}^2-4*{a1}*{c1})^0.5)/(2*{a1})}\\) &nbsp; or &nbsp; \\(x=\\simplify{(-{b1}- ({b1}^2-4*{a1}*{c1})^0.5)/(2*{a1})}\\)</p>", "preamble": {"css": "", "js": ""}, "variables": {"a1": {"name": "a1", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(1..6#1)"}, "b1": {"name": "b1", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(16..25#1)"}, "c1": {"name": "c1", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(1..10#1)"}}, "tags": [], "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}