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

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

The question is:
If x2 + 4ax + 3 = 0 and 2x2 + 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!

2. You can make a the subject of formula for each of the two equations.

Then equate both for x. You should get $\displaystyle x = \pm 3$

Substitute this value in any equation and you should get $\displaystyle a = \mp 1$

3. Nice one Unk; now relax to some classical music:
YouTube - Ahab the Arab - Ray Stevens

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# if x^2 4ax 3a and 2x^2 3ax-9

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