MathDB
polynomial

Source: Ireland 1993

June 29, 2009
algebrapolynomialalgebra proposed

Problem Statement

Let f(x)\equal{}x^n\plus{}a_{n\minus{}1} x^{n\minus{}1}\plus{}...\plus{}a_0 (n≥1) (n \ge 1) be a polynomial with real coefficients such that |f(0)|\equal{}f(1) and each root α \alpha of f f is real and lies in the interval [0,1] [0,1]. Prove that the product of the roots does not exceed 12n \frac{1}{2^n}.
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