IMO 1969 LL USS66

Origin: USS

Problem

(a) Prove that if 0 \leqa0 \leqa1 \leqa2, then (a0 + a1x −a2x2)2 \leq(a0 + a1 + a2)2  1 + 1 2x + 1 3x2 + 1 2x3 + x4  . (b) Formulate and prove the analogous result for polynomials of third degree.