Mathematics - Quadratic Equation Question with Solution | TestHub

Let the roots are $\alpha$ and $2\alpha$

$\Rightarrow \alpha +2\alpha =\frac{1-3\mathrm{a}}{{\mathrm{a}}^2-5\mathrm{a}+3}\text{ and }\alpha \cdot 2\alpha =\frac{2}{{\mathrm{a}}^2-5\mathrm{a}+3}$

$\begin{array}{rlrlr}& \Rightarrow 2\left[\frac{1}{9}\frac{(1-3a{)}^2}{{\left(a^2-5a+3\right)}^2}\right]=\frac{2}{a^2-5a+3}& & & \end{array}$

$\Rightarrow 9a^2-6a+1=9a^2-45a+27$

$\Rightarrow 39a=26\Rightarrow \frac{2}{3}$