Use a quadratic equation to find two real numbers with a sum of -43 and a product of 306.

Question

Use a quadratic equation to find two real numbers with a sum of -43 and a product of 306.

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Thiên Thanh 3 years 2021-08-29T05:19:51+00:00 1 Answers 69 views 0

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  1. diemkieu
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    2021-08-29T05:20:59+00:00
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    Answer:

    Real numbers = 39 and 9

    Step-by-step explanation:

    The standard form of a quadratic equation is ax² + bx + c = 0

    Given the following data;

    a = 1

    b = -43

    c = 306

    Quadratic equation formula is;

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

    Substituting into the equation, we have;

    x = \frac {-(-43) \; \pm \sqrt {43^{2} - 4*1*306}}{2*1}

    x = \frac {43 \pm \sqrt {1849 - 1224}}{2}

    x = \frac {43 \pm \sqrt {625}}{2}

    x = \frac {43 \pm 25}{2}

    x_{1} = \frac {43 + 25}{2}

    x_{1} = \frac {68}{2}

    x_{1} = 39

    x_{2} = \frac {43 - 25}{2}

    x_{2} = \frac {18}{2}

    x_{2} = 9

    Therefore, the two real numbers are 39 and 9.

    The quadratic equation now becomes;

    x² – 43x + 306 = (x – 39)(x – 9) = 0

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