Zeroes And Local Extremum Of Polynomials

Question

Prove that if $p(x)$ is a polynomial such that it has at least one zero and let $a$ and $b$ be the zeroes of polynomial such that $b \geq a$ and there is no $x$ with $x<a$,or $x>b$ such that $p(x)=0$, then $p(x)$ has no local Extremum for $x<a$ or $x>b$.