Use M.V.T to show that polynomial p(x) of degree n>= 1 has at most n roots. Hint : the proof proceeds by induction on the degree of p(x)
I don't know how to proof by induction but here is my approach on this question.
1. we know that polynomial of degree 1 will have at most 1 root and we want to show that n+1 degree => at most n+1 root.
2. so i try proof by contradiction by assume p(x) of degree n+1 will have at least n+2 root.
by M.V.T (Rolle's theorem), this assumption implies that p‘(x) has at least n+1 roots.But p'(x) is a polynomial of degree (n+1) - 1 , so it can not have more than n roots. So it contradict my assumption. p(x) of degree n+1 has at most n+1 roots?