Mathematics - Quadratic Equation Question with Solution | TestHub

Let the roots of the equation be $\alpha$ and $3\alpha$. From Vieta's formulas, the sum of the roots is $\alpha +3\alpha =4\alpha =8$, which implies $\alpha =2$. The product of the roots is $\alpha \cdot (3\alpha )=3{\alpha }^2=k$. Substituting $\alpha =2$, we get $k=3(2^2)=3(4)=12$.