Question 66
(USS 3) (a) Prove that if $0\le a_0\le a_1\le a_2$, then
$$(a_0+a_1x-a_2x^2)^2\le(a_0+a_1+a_2)^2\left(1+\frac12x+\frac13x^2+\frac12x^3+x^4\right).$$
(b) Formulate and prove the analogous result for polynomials of third degree.
$$(a_0+a_1x-a_2x^2)^2\le(a_0+a_1+a_2)^2\left(1+\frac12x+\frac13x^2+\frac12x^3+x^4\right).$$
(b) Formulate and prove the analogous result for polynomials of third degree.