Quote:
Originally Posted by CaptainBlack  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 |
A simple example of a polynomial satisfying the conditions of this problem is:
f(x) = (x+1)^2 = x^2 + 2x +1
where n=2, and f(2) = 9 = 3^2 <= 3^2
as expected.
RonL