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P(x) \geq (x + 1)^{n}

Source: Croatian NMC 2005, 4 th Grade

May 7, 2007
algebrapolynomiallimitinequalitiesalgebra unsolved

Problem Statement

Let P(x)P(x) be a monic polynomial of degree nn with nonnegative coefficients and the free term equal to 11. Prove that if all the roots of P(x)P(x) are real, then P(x)≥(x+1)nP(x) \geq (x+1)^{n} holds for every x≥0x \geq 0.
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