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Maximum value of lambda

Source: Chinese MO 1999

March 19, 2012
algebrapolynomialinequalities proposedinequalities

Problem Statement

Determine the maximum value of λ\lambda such that if f(x)=x3+ax2+bx+cf(x) = x^3 +ax^2 +bx+c is a cubic polynomial with all its roots nonnegative, then f(x)≥λ(x−a)3f(x)\geq\lambda(x -a)^3 for all x≥0x\geq0. Find the equality condition.
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