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Thread: Factoring

  1. #1
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    Factoring

    If one root of the equation 2x^2 + 10x + k = 0 is -2, what is the other root?
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  2. #2
    Senior Member eumyang's Avatar
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    Plug in -2 for x and solve for k:
    $\displaystyle \begin{aligned}
    2x^2 + 10x + k &= 0 \\
    2(-2)^2 + 10(-2) + k &= 0 \\
    8 - 20 + k &= 0 \\
    -12 + k &= 0 \\
    k &= 12
    \end{aligned}$

    For a quadratic equation $\displaystyle ax^2 + bx + c = 0$ the sum of the two roots (I'll call them r1 and r2) is -b/a:
    $\displaystyle \begin{aligned}
    r_1 + r_2 &= -\frac{10}{2} \\
    -2 + r_2 &= -5 \\
    r_2 &= -3
    \end{aligned}$

    So the other root is -3.
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  3. #3
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    Quote Originally Posted by MATNTRNG View Post
    If one root of the equation 2x^2 + 10x + k = 0 is -2, what is the other root?
    The roots are

    $\displaystyle \displaystyle\huge\frac{-10\pm\sqrt{.....}}{4}$

    For one of these to be $\displaystyle -2=-\frac{8}{4}$

    $\displaystyle \sqrt{...}=2$

    Therefore the other root is

    $\displaystyle \displaystyle\huge\frac{-10-2}{4}$
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