Mathematics - Quadratic Equation Question with Solution | TestHub

Here Let $x-\alpha$ is the common factor then $\mathrm{x}=\alpha$ is root of the corresponding equation $\therefore {\alpha }^2-11\alpha +a=0$ ${\alpha }^2-14\alpha +2\mathrm{a}=0$ Subtracting $3\alpha -a=0\Rightarrow \alpha =a/3$ Hence $\frac{a^2}{9}-11\frac{a}{3}+a=0,a=0$ or $a=24$ since $\mathrm{a}\ne 0,\mathrm{a}=24$ $\therefore$ the common factor of $\{\begin{array}{l}{x}^2-11x+24\\ x^2-14x+48\end{array}$ is clearly $x-8$