Dont know how to answer the more general forms of these questions using Rolle's Theorem and mean value theorem, for example;

- Show that the equation $\displaystyle x^3-15x+c=0$ has at most one root in the interval $\displaystyle [-2,2]$

- Show that a polynomial of degree 3 has at most three real roots

- Show that a polynomial of degree n has at most n real roots.