Question

If $x^2+7ax+40$ and $x^2+2ax-60$ have a common factor , then find the value of a,

• A. $\pm 1$
• B. $\pm 3$
• C. $0$
• D. $\pm 2$

Answer 1

The correct option is D $\pm 2$

$x^2+7ax+40\text{and}{x}^2+2ax-60\text{have a}$

$\text{common factor}$

$x^2+7ax+40$

$-x^2+2ax-60$

$----------$

$5ax+100$

$\text{Therefore,}ax=-20\text{, Put the value in}$

$\text{above equations}$

$x^2+7(-20)+40=0$

$x=\pm 10$

$\text{Therefore,}a=\mp 2$