Question

If the two polynomials $x^2-11x+a$ and $x^2-14x+2a$ have a common factor, then $a=$

• A. $0,24$
• B. $24$
• C. $0$
• D. $0,3$

Answer 1

The correct option is A $0,24$

Exprssions $x^2-11x+a$ and $x^2-14x+2a$ will have a common factor, then
$\Rightarrow \frac{x^2}{-22a+14a}=\frac{x}{a-2a}=\frac{1}{-14+11}$

$\Rightarrow \frac{x^2}{-8a}=\frac{x}{-a}=\frac{1}{-3}$
$\Rightarrow x^2=\frac{8a}{3}\&x=\frac{a}{3}$

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

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