Hi, 1. The problem statement, all variables and given/known data I am asked to prove that given all roots of a polynomial P of order n>=2 are real, then all the roots of its derivative P' are necessarily real too. I am permitted to assume that a polynomial of order n cannot have more than n real roots. 2. Relevant equations 3. The attempt at a solution I have tried proving that using induction, but got stuck. I'd appreciate some assistance.