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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.

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# Homework Help: Roots of derivative of polynomial.

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