IMO 1971 LL YUG55

Prove that the polynomial x4 + \lambdax3 + µx2 + \nux + 1 has no

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IMO 1971 LL YUG55

Origin: YUG

Problem

Prove that the polynomial x4 + \lambdax3 + µx2 + \nux + 1 has no real roots if \lambda, µ, \nu are real numbers satisfying |\lambda| + |µ| + |\nu| \leq \sqrt 2.