// Numbas version: exam_results_page_options
{"name": "Solving quadratic equations 1(c)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "functions": {}, "type": "question", "preamble": {"css": "", "js": ""}, "statement": "<p>The following equation can be converted into a quadratic equation:</p>\n<p style=\"padding-left: 30px;\">\\(\\var{a1}x+\\frac{\\simplify{{a1}*{b1}*{c1}}}{x}=\\simplify{{a1}*({b1}+{c1})}\\)</p>", "showQuestionGroupNames": false, "name": "Solving quadratic equations 1(c)", "tags": [], "variable_groups": [], "variablesTest": {"maxRuns": "1", "condition": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solving quadratic equations using a formula</p>"}, "advice": "<p>\\(\\var{a1}x+\\frac{\\simplify{{a1}*{b1}*{c1}}}{x}=\\simplify{{a1}*({b1}+{c1})}\\)</p>\n<p>We clear the fraction in the equation by multiplying across by \\(x\\)</p>\n<p>\\(\\var{a1}x^2+\\simplify{{a1}*{b1}*{c1}}=\\simplify{{a1}*({b1}+{c1})}x\\)</p>\n<p>Bringing all the terms to the left hand side and putting them in order of their powers of \\(x\\) gives</p>\n<p>\\(\\var{a1}x^2-\\simplify{{a1}*({b1}+{c1})}x+\\simplify{{a1}*{b1}*{c1}}=0\\)</p>\n<p>The formula for solving a quadratic equation of the form &nbsp;\\(ax^2+bx+c=0\\) &nbsp;is given by</p>\n<p style=\"padding-left: 30px;\">\\(x=\\frac{-b\\pm \\sqrt{b^2-4ac}}{2a}\\)</p>\n<p>In this example &nbsp;\\(a=\\var{a1},\\,\\,\\,b=\\simplify{+-{a1}*({b1}+{c1})}\\) &nbsp;and &nbsp;\\(c=\\simplify{{a1}*{b1}*{c1}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(x=\\frac{\\var{b}\\pm \\sqrt{(-\\var{b})^2-4*\\var{a1}*\\var{c}}}{2*\\var{a1}}\\)</p>\n<p style=\"padding-left: 30px;\">\\(x=\\frac{\\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;or &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>", "ungrouped_variables": ["a1", "b1", "c1", "b", "c"], "variables": {"a1": {"templateType": "randrange", "definition": "random(1..6#1)", "description": "", "name": "a1", "group": "Ungrouped variables"}, "c1": {"templateType": "randrange", "definition": "random(1..10#1)", "description": "", "name": "c1", "group": "Ungrouped variables"}, "b": {"templateType": "anything", "definition": "{a1}*({b1}+{c1})", "description": "", "name": "b", "group": "Ungrouped variables"}, "b1": {"templateType": "randrange", "definition": "random(11..25#1)", "description": "", "name": "b1", "group": "Ungrouped variables"}, "c": {"templateType": "anything", "definition": "{a1}*{b1}*{c1}", "description": "", "name": "c", "group": "Ungrouped variables"}}, "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "questions": [], "pickQuestions": 0}], "parts": [{"showCorrectAnswer": true, "variableReplacements": [], "scripts": {}, "type": "gapfill", "prompt": "<p>Type in the greater of the two values that satisfies the equation.&nbsp;</p>\n<p style=\"padding-left: 30px;\">\\(x = \\)&nbsp;[[0]]</p>\n<p>Type in the lesser of the two values that satisfies the equation.&nbsp;</p>\n<p style=\"padding-left: 30px;\">\\(x = \\)&nbsp;[[1]]</p>", "marks": 0, "gaps": [{"variableReplacements": [], "marks": 1, "scripts": {}, "allowFractions": false, "showCorrectAnswer": true, "minValue": "{b1}", "strictPrecision": false, "type": "numberentry", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{b1}", "precisionPartialCredit": 0, "precision": "3", "showPrecisionHint": true, "precisionType": "dp", "variableReplacementStrategy": "originalfirst"}, {"variableReplacements": [], "marks": 1, "scripts": {}, "allowFractions": false, "showCorrectAnswer": true, "minValue": "{c1}", "strictPrecision": false, "type": "numberentry", "correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "maxValue": "{c1}", "precisionPartialCredit": 0, "precision": "3", "showPrecisionHint": true, "precisionType": "dp", "variableReplacementStrategy": "originalfirst"}], "variableReplacementStrategy": "originalfirst"}], "extensions": [], "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/"}]}