# To Yosheph: About a polynomial

Problem.  Let $f(x)=x^3-6x^2+17x$ and $a,b\in\mathbb{C}$ such that $f(a)=16, f(b)=20$. Find $a+b$.

A hint. Assume that $a+b=h$, where $h$ is what you are finding! Then $f(a)=16$ and $f(h-a)=20$,  therefore  $a$ is a common root of two polynomials $f(x)-16$ and $f(h-x)-20$.