PUMaC 2025 · 个人决赛（B 组） · 第 3 题

PUMaC 2025 — Individual Finals (Division B) — Problem 3

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 1

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