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Math Help - trunomial

  1. #1
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    trunomial

    Given x^3 - 10x^2 + ax + b = 0 and two if its roots are 5 and 2, find a and b.
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  2. #2
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    Quote Originally Posted by Mr_Green View Post
    Given x^3 - 10x^2 + ax + b = 0 and two if its roots are 5 and 2, find a and b.
    Let the thrird root be u, then:

    (x-u)(x-5)(x-2) = x^3 - x^2 (u + 7) + x (7u + 10) - 10u

    but this is equal to x^3 - 10x^2 + ax + b, so equating the coefficients of
    x^2, we see that u=3.

    So:

    x^3 - 10 x^2 +31 x - 30 = x^3 - 10x^2 + ax + b

    so b=30, and a=31.

    RonL
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