// Numbas version: exam_results_page_options
{"name": "Solve a Quadratic Equation of the form  $ ax ^ 2 + bx + c = 0 \\,$ by Factorisation ONE Question (Doesnt work)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "d"], "name": "Solve a Quadratic Equation of the form  $ ax ^ 2 + bx + c = 0 \\,$ by Factorisation ONE Question (Doesnt work)", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p><strong>Direct Factorisation.</strong></p>\n<p>Factorise&nbsp;the quadratic expression :&nbsp;$\\simplify{{a*b} * x ^ 2 + ( {-b*c-a * d}) * x + {c * d}}$ by trial and error.....</p>\n<p>We get: $\\simplify{{a*b} * x ^ 2 + ( {-b*c-a * d}) * x + {c * d} = ({a} * x + { -c}) * ({b} * x + { -d})}$</p>\n<p>Now we&nbsp;solve the quadratic equation: $\\simplify{({a} * x + { -c}) * ({b} * x + { -d})}=0&nbsp;$ &nbsp; as follows:</p>\n<p>We conclude from the previous equation that:&nbsp;</p>\n<p>$\\simplify{({a} * x + { -c})}&nbsp;=0$ &nbsp; &nbsp; &nbsp;or&nbsp; &nbsp;$\\simplify{({b} * x + { -d})}=0$ &nbsp; giving&nbsp;</p>\n<p>$\\simplify{{a} * x =&nbsp;{c}}$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; or &nbsp; $\\simplify{{b} * x =&nbsp;{d}}$ &nbsp; &nbsp;so</p>\n<p>$\\simplify{x ={c}/{a}}&nbsp;$ &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; or &nbsp; &nbsp;$\\simplify{ x ={d}/{b}}&nbsp;$ &nbsp;</p>\n<p>The <strong>roots</strong> are, in ascending order, &nbsp;$ x = \\simplify[fractionNumbers]{{min({c}/{a},{d}/{b})}}$ &nbsp;and &nbsp;$ x = \\simplify[fractionNumbers]{{max({c}/{a},{d}/{b})}}$&nbsp;</p>\n<p></p>\n<p></p>\n<p></p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"]}, "parts": [{"prompt": "<p>\\[\\simplify{{a*b} * x ^ 2 + ( {-b*c-a * d}) * x + {c * d}}=0\\]</p>\n<p>The <strong>factors</strong> are: &nbsp;[[0]]</p>\n<p>The <strong>roots</strong> are: &nbsp; <em>Smallest</em> Root: &nbsp;[[1]]&nbsp; &nbsp; <em>Largest</em> Root: &nbsp;&nbsp;[[2]]&nbsp;</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Factorise the expression into two factors.</p>", "showStrings": false, "strings": ["^", "x*x", "x x", "x(", "x (", ")x", ") x"], "partialCredit": 0}, "vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.0001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "((({a} * x) + {( - c)}) * (({b} * x) + {( - d)}))", "marks": "4", "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme", "musthave": {"message": "<p>factorise the expression into two factors</p>", "showStrings": false, "strings": ["(", ")"], "partialCredit": 0}}, {"allowFractions": true, "variableReplacements": [], "maxValue": "min([{c}/{a},{d}/{b}])", "minValue": "min([{c}/{a},{d}/{b}])", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": true, "variableReplacements": [], "maxValue": "max([{c}/{a},{d}/{b}])", "minValue": "max([{c}/{a},{d}/{b}])", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": false, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "extensions": [], "statement": "<p><strong></strong></p>\n<p><strong>Solve the following quadratic equation by <em>factorisation</em></strong>.</p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(1..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-3..3)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "if(a=1,random(2..3),random(1..2))", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(-2..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "<p>Solve&nbsp;$\\displaystyle{ax ^ 2 + bx + c=0}$ by factorisation.&nbsp;</p>", "licence": "All rights reserved"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}]}]}], "contributors": [{"name": "Clare Lundon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/492/"}]}