Question

$x^2-11x+a$ and $x^2-14x+2a$ will have a common factor, if a =

• A. 24
• B. 0,24
• C. 3,24
• D. 0,3

Answer 1

The correct option is B

0,24

Exprssions are $x^2-11x+a$ and $x^2-14x+2a$ will have a common factor, then

⇒ $\frac{x^2}{-22a+14a}=\frac{x}{a-2a}=\frac{1}{-14+11}$

⇒ $\frac{x^2}{-8a}=\frac{x}{-a}=\frac{1}{-3}$ ⇒ $x^2=\frac{8a}{3}andx=\frac{a}{3}$

⇒ $(\frac{a}{3}{)}^2=\frac{8a}{3}$ ⇒ $\frac{a^2}{9}=\frac{8a}{3}$ ⇒ a = 0, 24.

Alternate Method : We can check by putting the values of a from the options.