In this problem you will use Rolle's theorem to determine whether it is possible for the function [math] to have two or more real roots (or, equivalently, whether the graph of [math] crosses the [math]-axis two or more times).

Suppose that [math] has at least two real roots. Choose two of these roots and call the smaller one [math] and the larger one [math]. By applying Rolle's theorem to [math] on the interval [math], there exists at least one number [math] in the interval [math] so that [math] .

The values of the derivative [math] are always , and therefore it is for [math] to have two or more real roots.