Question

If $x^2+7ax+40=0$ and $x^2+2ax-60=0$ have a common root, then the value of a is

• A. $\pm 1$
• B. $\pm 2$
• C. $\pm 3$
• D. $\pm 4$

Answer 1

The correct option is B $\pm 2$

$x^2+7ax+40=0$ and $x^2+2ax-60=0$
Let the common root be m, then
$m^2+7am+40=0,m^2+2am-60=0$
Subtracting both the equations,
5am + 100 =0
$m=\frac{-20}{a}$
Put the value in $m^2+7am+40=0$
$\frac{400}{a^2}+7a\frac{-20}{a}+40=0$
$400-140a^2+40a^2=0$
$100a^2-400=0$
$a=\pm 2$