Mathematics - Quadratic Equation Question with Solution | TestHub

If $\alpha ,\beta$ are the roots of the equation $\lambda \left(x^2-x\right)+x+5=0$ and if ${\lambda }_1\&{\lambda }_2$ are two values of $\lambda$ for which the roots $\alpha ,\beta$ are related by $\frac{\alpha }{\beta }+\frac{\beta }{\alpha }=\frac{4}{5}$, then the value of $\frac{{\lambda }_1}{{\lambda }_2}+\frac{{\lambda }_2}{{\lambda }_1}=\left(255-{\mathrm{k}}^2\right)$ then $|\mathrm{k}|$ is