Polynomial at least one root between 0 and 1 – math.stackexchange.com

$p(x)=a_0+a_1x+...a_nx^n$ with $a_0+a_1/2+...a_n/(n+1)=0$. Heuristically, I feel like this should have at least one root between 0 and 1, because at least one of the coefficients will have a ...

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