// Numbas version: exam_results_page_options {"name": "Solving quadratic equations 1(a)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "statement": "

There are two values that satisfy the quadratic equation:

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\$$\\var{a1}x^2+\\simplify{{{a1}*{b1}*{c1}}}=\\simplify{{a1}*{b1}+{a1}{c1}}x\$$

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Type in the greater of the two values that satisfies the equation.

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Input your answer correct to three decimal places.  \$$x = \$$ [[0]]

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Type in the lesser of the two values that satisfies the equation.

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Input your answer correct to three decimal places.  \$$x = \$$ [[1]]

Solving quadratic equations using a formula,

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The formula for solving a quadratic equation of the form  \$$ax^2+bx+c=0\$$  is given by

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\$$x=\\frac{-b\\pm \\sqrt{b^2-4ac}}{2a}\$$

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In this example  \$$a=\\var{a1},\\,\\,\\,b=\\simplify{+-{a1}*({b1}+{c1})}\$$  and  \$$c=\\simplify{{a1}*{b1}*{c1}}\$$

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\$$x=\\frac{\\var{b}\\pm \\sqrt{(-\\var{b})^2-4*\\var{a1}*\\var{c}}}{2*\\var{a1}}\$$

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\$$x=\\frac{\\var{b}\\pm \\sqrt{\\simplify{{b}^2-4*{a1}*{c}}}}{\\simplify{2*{a1}}}\$$

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\$$x=\\simplify{{b}+({b}^2-4*{a1}*{c})^0.5}/\\simplify{2*{a1}}=\\simplify{({b}+({b}^2-4*{a1}*{c})^0.5)/(2*{a1})}\$$        or        \$$x=\\simplify{{b}-({b}^2-4*{a1}*{c})^0.5}/\\simplify{2*{a1}}=\\simplify{({b}-({b}^2-4*{a1}*{c})^0.5)/(2*{a1})}\$$

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