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Math Help - 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:
    \begin{aligned}<br />
2x^2 + 10x + k &= 0 \\<br />
2(-2)^2 + 10(-2) + k &= 0 \\<br />
8 - 20 + k &= 0 \\<br />
-12 + k &= 0 \\<br />
k &= 12<br />
\end{aligned}

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

    So the other root is -3.
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  3. #3
    MHF Contributor
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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\huge\frac{-10\pm\sqrt{.....}}{4}

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

    \sqrt{...}=2

    Therefore the other root is

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