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0751

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June 9, 2008
algebrapolynomialinequalitiesVietaproduct of rootsabsolute value

Problem Statement

Find all real polynomials g(x) g(x) of degree at most n \minus{} 3, n≥3 n\geq 3, knowing that all the roots of the polynomial f(x) \equal{} x^n \plus{} nx^{n \minus{} 1} \plus{} \frac {n(n \minus{} 1)}2 x^{n \minus{} 2} \plus{} g(x) are real.
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