How to find sum of coefficients of a polynomial?
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The sum of the coefficients is just the value of the polynomial in 1, hence if the polynomial is monic with roots in n1,…,nk, then p(1)=(1−n1)⋅… ⋅(1−nk). put x=1, then 0=1+a99+a98+... a1+a0.
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