Two Quadratic Equations With a Common Root, and an Unknown Coefficient

**The question is:**

If x^{2} + 4ax + 3 = 0 and 2x^{2} + 3ax – 9 = 0 have a common root, then the value of ‘a’ is?

(A) +3,-3

(B) +1,-1

(C) Only 1

(D) +2,-2

**My approach**

At first, I simply plugged in every option and figured out the answer, but, I want to know if there is any way I could have done this had I not been given options?

I started out by considering 'b' as the common root, substituting it for 'x' in both the equations, and then equating the equations. Then...I got stuck...and I've been stuck ever since...

Any help would be really appreciated.

Thanks!