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?
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