Let $p$ be a polynomial of degree $n$. Prove that it has at most n zeros.
Use induction and mean value theorem.
I don't understand how to do the induction. I used $n=0$ for the base case which is obvious and then I assumed that for degree $n$ that the polynomial had at most n roots. Then I was trying to prove that for $n+1$ it had at most $n+1$ roots.