If x=-2 is the common solution of the quadratic . . .

Question :  If x=-2 is the common solution of the quadratic equation ax²+x-3a=0 and x²+bx+b=0, then find the value of a²b.

Doubt by CBSE 

Solution : 

ax²+x-3a=0

a(-2)²+(-2)-3a=0

4a-2-3a=0

a-2=0

a=2

Also

x²+bx+b=0

(-2)²+b(-2)+b=0
4-2b+b=0
4-b=0

-b=-4
b=4

Now, 
a²b
=(2)²(4)
=4(4)
=16

Hence, a²b=16