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)

Let g (x) = a0x + A1 / 2 x & # 178; +... + an / (n + 1) x ^ (n + 1)
Then G (0) = g (1) = 0
From Rolle's mean value theorem
There exists C ∈ (0,1) such that G '(c) = f (c) = 0
Get proof
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