Question

If $x^2-11x+a$ and $x^2-14x+2a$ have a common root, then $a$ is equal to

• A. $24$
• B. $1$
• C. $2$
• D. $12$

Answer 1

Answer: (A)

$24$

Let $\alpha$ is the common root
Then from ${\alpha }^2-11\alpha +\alpha =0,{\alpha }^2-14\alpha +2\alpha =0$

$\frac{{\alpha }^2}{-22\alpha +14\alpha }=\frac{\alpha }{\alpha -2\alpha }=\frac{1}{-14+11}$ $($ Using cramer rule $)$

${\alpha }^2=\frac{-8\alpha }{-3}=\frac{8}{3}\alpha$

And $\alpha =\frac{-\alpha }{-3}=\frac{a^2}{3}\Rightarrow {\alpha }^2=\frac{{\alpha }^2}{9}$

$\therefore \frac{8}{3}a=\frac{{\alpha }^2}{9}\Rightarrow a=24.$