I have to show that Rolle's theorem can be used to prove that the function 2x5 − 5x4 + ax cannot have five distinct real zeros. I know that Rolle's theorem means that if f(a)=f(b)=0 there must be some x value c between a and b such that f'(c)=0. I am unsure of how to do this, would i show that the derivative does not equal zero 4 times and then use Rolle's theorem to say therefore there must be less than 5 zeros for the function.

Would this be a way to do it? If not how would i do it?

Thanks.