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Quadratic formula - GMAT prep - Hard

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by lazarogb » Sun Dec 09, 2012 6:15 am
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.
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by Brent@GMATPrepNow » Sun Dec 09, 2012 9:19 am
lazarogb wrote: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.
2x^2+5x=12 is a quadratic equation, so let's set it equal to zero to get:
2x^2 + 5x - 12 = 0
Factor: (2x-3)(x+4) = 0
So, 2x-3 = 0
or x+4 = 0

If 2x-3 = 0, then x = 3/2
If x+4 = 0, then x = -4

So, the larger root (3/2) exceeds the smaller root (-4) by 11/2 [since 3/2 - (-4) = 11/2]

Answer = E

Cheers,
Brent
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by kevincanspain » Sun Dec 09, 2012 12:30 pm
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)
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by theachiever » Sun Dec 09, 2012 11:57 pm
Direct formula application using

-b+/-sqrtb^2-4ac/2a

Substitute the corresponding values from the equation and subtract the roots which gives you E
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