PUMaC 2025 · 个人决赛（A 组） · 第 1 题

PUMaC 2025 — Individual Finals (Division A) — Problem 1

Let λ be the maximum value of λ such that for all cubic polynomials P ( x ) = x + ax + bx + c 3 whose zeros are all real and nonnegative, then P ( x ) ≥ λ ( x − a ) for all x ≥ 0. Prove that 1 ∗ λ = − . 27

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