# A theorem to rule them all

Calculus Level pending

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 $$a_0 + a_1 z + \cdots + a_n z^n = 0$$.

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