For numbers a1,....,an, define
p(x) = a1x +a2x^2+....+anx^n for all x. Suppose that:
(a1)/2 + (a2)/3 +....+ (an)/(n+1) = 0
Prove that there is some point x in the interval (0,1) such that p(x) = 0© BrainMass Inc. brainmass.com March 4, 2021, 5:48 pm ad1c9bdddf
An integral and Mean Value Theorem are used to provide a real analysis proof.