algeBRA!!!

What is the sum of the rational roots of f(x)=x^3−4x^2+16x−39?

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  1. I tried x = ±1 and ±3
    it worked for x = 3, so x-3 is a factor and x=3 is a root
    by synthetic division I got
    x^3−4x^2+16x−39 = (x-3)(x^2 - x + 13)

    x^2 - x + 13 does not factor over the rationals, so there are no other rational roots

    the sum would simply be 3

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