Question

If $x^2-11x+a=0$ and $x^2-14x+2a=0$ have a common factor, then $a$ is equal to

• A. $24$
• B. $1$
• C. $2$
• D. $12$

Answer 1

Answer: (A)

$24$

Let $\alpha$ be common root.

Given eqaution:

$x^2-11x+a=0$ and $x^2-14x+2a=0$

${}^{\prime }{\alpha }^{\prime }$ satisfies both the equation.

${\alpha }^2-11\alpha +a=0$ and

${\alpha }^2-14\alpha +2a=0$

$\frac{{\alpha }^2}{-22a-(-14a)}=\frac{\alpha }{a-2a}=\frac{1}{-14-(-11)}$

$\Rightarrow \frac{{\alpha }^2}{-8a}=\frac{\alpha }{-a}\Rightarrow \alpha =8$

Putting value of $\alpha$ in equation we get,

$8^2-11\times 8+a=0$

$\Rightarrow -24+a=0$

$\Rightarrow a=24$

Hence, A is the correct option.