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) a0>0, an>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)≥0 for all real values x.
Laurentiu Panaitopol algebrapolynomialinequalitiesvectorinequalities proposed