I'd say it's not likely that you'll see such a question on the GMAT simply because the quadratic equations on the test are pretty straightforward. I'm also getting two answers... Maybe someone can tell me what I'm doing wrong here.
First off, what are the roots of equation 6*x^2 - 17x + 12?
To find these, we'll calculate the discriminant of the equation: 17^2 - 4*6*12 = 289 - 288 = 1 (this is an instance where you would highly benefit from knowing the squares up to 20). This means that the roots of the equation will be:
1. (17 - 1)/12 = 16/12 = 4/3
2. (17 + 1)/12 = 18/12 = 3/2
You may notice that the coefficient of x^2 is 6, which is 2*3, or, in other words, the denominators of the two roots. This might hint to the fact that the common root for the two equations is actually 4/3, since the coefficient of x^2 in 3*x^2 - 2x + p is 3. If you replace that you get:
3*(4/3)^2 - 2*(4/3) + p = 0
3*16/9 - 8/3 + p = 0
16/3 - 8/3 + p = 0
8/3 + p = 0
p = -8/3
Try with x = 3/2:
3*(3/2)^2 - 2*3/2 + p = 0
27/4 - 12/4 + p = 0
p = -13/4
That's why I'm saying you get two different results... or maybe I'm missing something.
