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No real roots if coefficients sum to less than root 2

Source:

January 1, 2011
algebrapolynomialalgebra proposed

Problem Statement

Prove that the polynomial x4+λx3+μx2+νx+1x^4+\lambda x^3+\mu x^2+\nu x+1 has no real roots if λ,μ,ν\lambda, \mu , \nu are real numbers satisfying ∣λ∣+∣μ∣+∣ν∣≤2|\lambda |+|\mu |+|\nu |\le \sqrt{2}
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