P(x) be any polynomial of degree at least 2

[ken1101]

Homework Statement

Let P(x) be any polynomial of degree at least 2, all of whose roots are real and distinct. Prove that all of the roots of P'(x) must be real. What happens if some of the roots of P are multiple roots?

Homework Equations

I think that question is related to the concept of least upper bound or mean value theorem. But i have no clue.

The Attempt at a Solution

 

[Office_Shredder]

What can you say must occur between any two roots of P(x)? Try drawing some polynomials and see if you can identify where the roots of P'(x) are based on the roots of P(x)