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Math Help - Quadratic equation

  1. #1
    Junior Member
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    Quadratic equation

    The equation: x^3 - 3x^2 - 10x + 24 = 0

    has roots: 2, "h" and "k"

    Determine a quadratic equation whose roots are "h" - "k" and "hk"

    How do you do it?




    The anwser is: x^2 + 5x -84 = 0
    Last edited by B-lap; October 19th 2008 at 04:39 PM.
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  2. #2
    Member
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    Oct 2008
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    I'm guessing that you can solve for h and k, by first dividing by x-2, and the factoring the resulting polynomial. Say that h = 3 and k = -4. Then h-k = 3-(-4) = 7. hk = -12. Create the two polynomials corresponding to the roots.
    (x-7)(x+12). Multiply it out to get the answer.

    (I didn't solve the polynomial, I worked backwards to get the answer, but the approach is the same.)
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