Thread: Problem 21
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Old March 12th, 2007, 01:15 PM
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Originally Posted by CaptainBlack View Post
Let the polynomial:

f(x) = x^n + a_1 x^{n-1} + ... + a_{n-1} x +1

with non-negative real coefficients a_1, .. , a_{n-1} have n real roots.

Prove that f(2) >= 3^n

RonL
No, I still have a contradiction.

Let
f(x) = x^2 + 0.0001*x + 1

Then
f(2) = 4 + 0.0001*2 + 1 = 5.0002
which is not greater than or equal to 3^2 = 9.

-Dan
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