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