MathDB

Let P(X) \equal{} a_{n}X^{n} \plus{} a_{n \minus{} 1}X^{n \minus{} 1} \plus{} \ldots \plus{} a_{1}X \plus{} a_{0} be a real polynomial of degree

n

. Suppose

n

is an even number and: a)

a_{0} > 0

a_{n} > 0

; b) a_{1}^{2} \plus{} a_{2}^{2} \plus{} \ldots \plus{} a_{n \minus{} 1}^{2}\leq\frac {4\min(a_{0}^{2} , a_{n}^{2})}{n \minus{} 1}. Prove that

P(x)\geq 0

for all real values

x

. Laurentiu Panaitopol

Problem Statement