# A theorem to rule them all

True or False?

Let $a_0, a_1 , \ldots , a_n$ be reals such that $\dfrac {a_0}1 + \dfrac{a_1}2 + \cdots + \dfrac{a_n}{n+1} = 0$, then there exists a real $z\in [0,1]$ such that $a_0 + a_1 z + \cdots + a_n z^n = 0$.

×