IMO 1986 LL GBR35

Establish the maximum and minimum values that the sum

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IMO 1986 LL GBR35

Origin: GBR

Problem

Establish the maximum and minimum values that the sum |a| + |b| + |c| can have if a, b, c are real numbers such that the maximum value of |ax2 + bx + c| is 1 for −1 \leqx \leq1.