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Math Help - Discriminant =(

  1. #1
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    Post Discriminant =(

    I need help on this question and quick ><

    Find the value of k for which 5 + 4x - x^2 = k, has equal roots.

    To just lets you's know, k=9.
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  2. #2
    Super Member angel.white's Avatar
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    Quote Originally Posted by xornr89 View Post
    I need help on this question and quick ><

    Find the value of k for which 5 + 4x - x^2 = k, has equal roots.

    To just lets you's know, k=9.
    -x^2+4x+5 = k

    -x^2+4x+5-k = 0

    -(x^2-4x-5+k) = 0

    By completing the square you know you want (x-2)^2 which returns x^2-4x+4

    so 4=-5+k ~~~~~~\Rightarrow ~~~~~~k=9

    substituting this in you get
    -(x^2-4x-5+9) = 0

    -(x^2-4x+4) = 0

    -(x-2)^2 = 0

    (x-2)^2 = 0

    \pm (x-2) = 0

    so x-2=0 and -(x-2)=0

    Both of these values return x=2, thus they are the same.
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  3. #3
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    Alternately we could do this with the discriminant formula..
    For equal roots, D = 0.
    x = -b - \frac {\sqrt{D}}{2 \cdot a}
    x = \frac {-4}{-2}
    So x = 2.
    Substituting..
    5 + 8 - 4 = 9
    k = 9.
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