Let A0 + A1 / 2 +... + an / (n + 1) = 0, and prove that the polynomial f (x) = A0 + a1x +... + anx ^ n has at least one zero point in (0,1)

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1. Polynomial f (x) = A0 + a1x + a2x ^ 2 +... + anx ^ n, it is proved that f (x) = 0 has n + 1 different roots, then f (x) is equal to 0
2. Given that a, B and C are the roots of the equation x ^ 3 + PX + q = 0, find a + B + C =?, and give the process and theoretical basis, It seems to have something to do with Veda's theorem, but I don't know how to use it But the answer is 0,
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