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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- Sep 28th 2008, 07:28 PMjuldancersolving 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? - Sep 28th 2008, 07:42 PMJhevon
yup

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

also recall that a cubic where the coefficient of is 1 can be written as where and are the roots (not necessarily all real) of the equation.

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

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