Problem Solving

By how much does the larger root of the equation 2x^2+5x=12 exceed the smaller root?

a) 5/2

b) 10/3

c) 7/2

d) 14/3

e) 11/2

OA E

I tried the normal factoring strategy trying out fraction that would fit but never reached anywhere. The OA from the gmat guys use the quadratic formula which I had never seen was needed in the past.

Does anyone know an easier way to solve this other than by the standard quadratic formula??

Thanks.

The vast majority of the quadratic equations in the GMAT are factorable, though ax^2 +bx + c is a bit more difficult to factor when |a| > 1


Technique ax^2 + bx + c = (ax + m )(ax + n)/a where mn = c and m + n = b



For example, given 6x^2 + 19x - 36

mn = 6(-36) m + n = 19

Factorize 6(-36) = - 2^3 x 3^3

m,n are -8 and 27

We get (6x - 8)(6x + 27)/6 = (3x - 4)(2x + 9)


Regarding 2x^2 + 5x - 12

mn = -24
m+n= 5

m,n = -3, 8

2x^2 +5x - 12 = (2x - 3)(2x + 8)/2 = (2x - 3)(x + 4)