If are the roots of the equation

MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials

Problem

If α,β\alpha,\beta are the roots of the equation λ(x2−x)+x+5=0\lambda(x^2-x)+x+5=0, and λ1\lambda_1 and λ2\lambda_2 are the two values of λ\lambda for which αβ+βα=45\frac\alpha\beta+\frac\beta\alpha=\frac45, find λ1λ2+λ2λ1\frac{\lambda_1}{\lambda_2}+\frac{\lambda_2}{\lambda_1}.

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