1. The problem statement, all variables and given/known data Prove that if f is a polynomial function of degree n, then f has at most n roots, i.e., there are at most n numbers a with f(a) = 0. 2. Relevant equations N/A 3. The attempt at a solution I know that I'm supposed to use induction on the degree of the polynomial. If we assume a polynomial of degree 0, then f(x) is a constant and has no real roots. Now I don't know how to use induction on that statement. It's very easy to know intuitively but I'm having a lot of trouble formalizing this into a proof. Any hints would be greatly appreciated. By the way, another question: what if f(x) = 0? How many roots does that have? Thanks.