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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