Easy one .

Algebra Level 4

lf \(\displaystyle\alpha\) and \(\displaystyle\beta\) are the roots of the equation \(\displaystyle\lambda (x^{2} +x) +x+5=0, \) and \(\displaystyle\lambda_{1}\) and \(\displaystyle\lambda_{2}\) are two values of \(\displaystyle\lambda\) for which \(\displaystyle\alpha\) , \(\displaystyle\beta\) are connected by the relation \(\displaystyle\frac{\alpha}{\beta}+\frac{\beta}{\alpha} =4 ,\) then what is the value of \(\displaystyle\frac{\lambda_{1}}{\lambda_{2}}+\frac{\lambda_{2}}{\lambda_{1}} ?\)

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