MathematicsHard129×since 2002Q5161Let λ≠0\lambda \ne 0λ=0 be a real number. Let α,β\alpha,\betaα,β be the roots of the equation 14x2−31x+3λ=014{x^2} - 31x + 3\lambda = 014x2−31x+3λ=0 and α,γ\alpha,\gammaα,γ be the roots of the equation 35x2−53x+4λ=035{x^2} - 53x + 4\lambda = 035x2−53x+4λ=0. Then 3αβ{{3\alpha } \over \beta }β3α and 4αγ{{4\alpha } \over \gamma }γ4α are the roots of the equationA7x2−245x+250=07{x^2} - 245x + 250 = 07x2−245x+250=0B49x2−245x+250=049{x^2} - 245x + 250 = 049x2−245x+250=0C49x2+245x+250=049{x^2} + 245x + 250 = 049x2+245x+250=0D7x2+245x−250=07{x^2} + 245x - 250 = 07x2+245x−250=0Check answerSkip