IMO 1982 LL VIE56

Let f(x) = ax2 + bx + c and g(x) = cx2 + bx + a. If |f(0)| \leq1,

imolonglistmathematicsolympiad

IMO 1982 LL VIE56

Origin: VIE

Problem

Let f(x) = ax2 + bx + c and g(x) = cx2 + bx + a. If |f(0)| \leq1, |f(1)| \leq1, |f(−1)| \leq1, prove that for |x| \leq1, (a) |f(x)| \leq5/4, (b) |g(x)| \leq2.