MathDB

55

Part of 1971 IMO Longlists

Problems(1)

No real roots if coefficients sum to less than root 2

Source:

1/1/2011
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}
algebrapolynomialalgebra proposed