Finding real root of polynomial degree n using MVT for integrals
I really need help for this problem. I don't even know how to start this problem. Anyway, here's the problem:
if a0, a1, a2,..., an are real numbers that satisfy (a0/1) + (a1/2) + (a2/3) +...+ (an/n+1) = 0
show that the equation a0 + a1x + a2x2 +...+ anxn = 0 has at least one real root.
I am forced to use mean value theorem for integrals. In fact, I can't even see a straight answer for this even without the MVT for integrals. I just know that both equations are continuous and differentiable all over because they're polynomials.
Re: Finding real root of polynomial degree n using MVT for integrals
Let and we have
By the MVT there exists such that