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The formula for solving a quadratic equation of the form \\(ax^2+bx+c=0\\) is given by
\n\\(x=\\frac{-b\\pm \\sqrt{b^2-4ac}}{2a}\\)
\nIn this example \\(a=\\var{a1},\\,\\,\\,b=\\var{b1}\\) and \\(c=\\var{c1}\\)
\n\\(x=\\frac{-\\var{b1}\\pm \\sqrt{\\var{b1}^2-4\\times\\var{a1}\\times\\var{c1}}}{2\\times\\var{a1}}\\)
\n\\(x=\\frac{-\\var{b1}\\pm \\sqrt{\\simplify{{b1}^2-4*{a1}*{c1}}}}{\\simplify{2*{a1}}}\\)
\n\\(x=\\simplify{(-{b1}+ ({b1}^2-4*{a1}*{c1})^0.5)/(2*{a1})}\\) or \\(x=\\simplify{(-{b1}- ({b1}^2-4*{a1}*{c1})^0.5)/(2*{a1})}\\)
", "variables": {"b1": {"definition": "random(16..25#1)", "description": "", "templateType": "randrange", "name": "b1", "group": "Ungrouped variables"}, "c1": {"definition": "random(1..10#1)", "description": "", "templateType": "randrange", "name": "c1", "group": "Ungrouped variables"}, "a1": {"definition": "random(1..6#1)", "description": "", "templateType": "randrange", "name": "a1", "group": "Ungrouped variables"}}, "tags": [], "functions": {}, "metadata": {"description": "Solving quadratic equations using a formula,
", "licence": "Creative Commons Attribution 4.0 International"}, "variable_groups": [], "rulesets": {}, "ungrouped_variables": ["a1", "b1", "c1"], "parts": [{"marks": 0, "type": "gapfill", "showCorrectAnswer": true, "variableReplacements": [], "prompt": "Type in the greater of the two values that satisfies the equation. Input your answer correct to three decimal places.
\n\\(x\\) = [[0]]
\nType in the lesser of the two values that satisfies the equation. Input your answer correct to three decimal places.
\n\\(x\\) = [[1]]
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\n\\(\\var{a1}x^2+\\var{b1}x+\\var{c1}=0\\)
", "variablesTest": {"maxRuns": "1", "condition": "b1^2>4*a1*c1"}, "preamble": {"js": "", "css": ""}, "type": "question", "contributors": [{"name": "David Wishart", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1461/"}]}]}], "contributors": [{"name": "David Wishart", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1461/"}]}