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Solution of a cubic

Source: INMO 2000 Problem 5

October 10, 2005
algebrapolynomialalgebra unsolved

Problem Statement

Let a,b,ca,b,c be three real numbers such that 1≥a≥b≥c≥01 \geq a \geq b \geq c \geq 0. prove that if λ\lambda is a root of the cubic equation x3+ax2+bx+c=0x^3 + ax^2 + bx + c = 0 (real or complex), then ∣λ∣≤1.| \lambda | \leq 1.
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