MathDB

root of polynomial

Source: 30-th Vietnamese Mathematical Olympiad 1992

February 17, 2007

algebrapolynomialalgebra unsolved

Problem Statement

Let

9 < n_{1} < n_{2} < \ldots < n_{s} < 1992

be positive integers and P(x) \equal{} 1 \plus{} x^{2} \plus{} x^{9} \plus{} x^{n_{1}} \plus{} \cdots \plus{} x^{n_{s}} \plus{} x^{1992}. Prove that if

x_{0}

is real root of

P(x)

then x_{0}\leq\frac {1 \minus{} \sqrt {5}}{2}.

Back to Problems View on AoPS