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| ax^2 + bx + c | <= 1 => |cx^2 + bx + a | <= r

Source: Czech-Polish-Slovak Junior Match 2018, Team p3 CPSJ

March 7, 2020
trinomialalgebrainequalities

Problem Statement

Calculate all real numbers rr with the following properties: If real numbers a,b,ca, b, c satisfy the inequality∣ax2+bx+c∣≤1 | ax^2 + bx + c | \le 1 for each x∈[−1,1]x \in [ - 1, 1], then they also satisfy the inequality ∣cx2+bx+a∣≤r| cx^2 + bx + a | \le r for each x∈[−1,1] x \in [- 1, 1].
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