Prove that if then Formulate and prove the analogous result for polynomials of third degree.
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$(USS 3)$ $(a)$ Prove that if $0 \le a_0 \le a_1 \le a_2,$ then $(a_0 + a_1x - a_2x^2)^2 \le (a_0 + a_1 + a_2)^2\left(1 +\frac{1}{2}x+\frac{1}{3}x^2+\frac{1}{2}x^3+x^4\right)$
$(b)$ Formulate and prove the analogous result for polynomials of third degree.
Izvor: Međunarodna matematička olimpijada, shortlist 1969
Školjka 
Prove that if 
then 
Formulate and prove the analogous result for polynomials of third degree.