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A root on unit circle

Source: Iranian National Olympiad (3rd Round) 2008

September 12, 2008
algebrapolynomialtrigonometryfunctioncalculusintegrationratio

Problem Statement

Prove that for n>0 n > 0 and a≠0 a\neq0 the polynomial p(z) \equal{} az^{2n \plus{} 1} \plus{} bz^{2n} \plus{} \bar bz \plus{} \bar a has a root on unit circle
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