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

Answer 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