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China Mathematical Olympiad 1992 problem1

Source: China Mathematical Olympiad 1992 problem1

September 29, 2013
inequalitiestriangle inequalityalgebra unsolvedalgebra

Problem Statement

Let equation xn+an−1xn−1+an−2xn−2+⋯+a1x+a0=0x^n+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\dots +a_1x+a_0=0 with real coefficients satisfy 0<a0≤a1≤a2≤⋯≤an−1≤10<a_0\le a_1\le a_2\le \dots \le a_{n-1}\le 1. Suppose that λ\lambda (∣λ∣>1|\lambda|>1) is a complex root of the equation, prove that λn+1=1\lambda^{n+1}=1.
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