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  1. #1
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    solving polynomial

    Find an integer d such that the equation x^3 + 4x^2 - 9x + d = 0 has two roots that are additive inverses of each other.

    Does anyone know how to do this?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by juldancer View Post
    Find an integer d such that the equation x^3 + 4x^2 - 9x + d = 0 has two roots that are additive inverses of each other.

    Does anyone know how to do this?
    yup

    first recall what additive inverses are. the additive inverse of a number a is -a.

    also recall that a cubic where the coefficient of x^3 is 1 can be written as (x - r_1)(x - r_2)(x - r_3) = 0 where r_1,r_2, and r_3 are the roots (not necessarily all real) of the equation.

    so let a and -a be the two special roots. call the other root b. thus we have

    (x - a)(x + a)(x - b) = 0

    \Rightarrow x^3 - bx^2 - a^2 x + ab = 0

    now equate coefficients to get the values of a and b, and hence find d
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