Hi All,

It looks like a number of the explanations take a more complex approach than what is needed. This question is based on FOIL-ing and Factoring rules; even though it looks a little "tough", the same rules still apply...

We're given 2X^2 + 5X = 12

We can rewrite that as....

2X^2 + 5X - 12 = 0

Now let's break this into it's two 'pieces'....

(X _ _ )(2X _ _ )

Now let's look at the '-12'....

This means that the two numbers could be....
1 and 12
2 and 6
3 and 4

And one number is + and the other is -

Since the middle term of the Quadratic is "5X", we need to 'play around' a bit with the possibilities....

1 and 12 are too far 'apart'
2 and 6 are both even, so we won't end up with 5X (since 5 is odd)

That just leaves us with 3 and 4....
(X + 4)(2X - 3) = 0

Now we can solve the Quadratic...

X = -4, +3/2

The prompt asks for the difference in the solutions...
(3/2) - (-4) = 11/2

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Re-writing the equation as follows:

\(2x^2 + 5x - 12 =0\)

The two factors of -24 (-12 x 2) are 8 & -3

So,\(2x^2 + 8x - 3x - 12 = 0\)

2x (x +4) -3 (x+4) = 0

(2x -3) (x+4) = 0

So \(x = \frac{3}{2}\) or x = -4
Distance between 3/2 & -4 =

\(\frac{3}{2} - (-4) = \frac{11}{2}\) (Answer = E)

You don't need to factor out anything for this question. Note that \((a-b)^2 = (a+b)^2-4ab\)

Now, the sum of the roots :\(\frac{-5}{2}\) and product of the roots :\(\frac{-12}{2}\)

Thus, \((a-b)^2 = \frac{25}{4}+4*6 = \frac{121}{4}\)

Thus, \((a-b) = \frac{11}{2}\)

E.
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TO DETERMINE THE ROOTS OF QUADRATIC EQUATION: \(ax^2+bx+c = 0\)

formula for root = \((-b+\sqrt{(b^2-4ac)})/2a\) and \((-b-\sqrt{(b^2-4ac)})/2a\)

now in your equation:\(2x^2+5x-12 = 0\)
\(a=2
b=5
c=-12\)

now when you will plug in the values in the formula

roots come out are = \(-4 and 3/2\)

subtracting smaller from bigger will give you \(11/2\)

hope it helps
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Note that \((a-b)^2 = (a+b)^2-4ab\)

How are you getting this? I thought \((a-b)^2 = a^2 -2ab+ b^2\)

\((a+b)^2-4ab = a^2+b^2+2ab-4ab = a^2 -2ab+ b^2\)

Hope this helps.
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Sorry for buggin', but I am still curious as to why you chose to manipulate \((a-b)^2 into (a+b)^2-4ab\) when you encountered this problem? Is there some sort of method/property that comes to mind? The study guides I am using doesn't really show this, but I would love to know

I chose this method only in this context . The question was asking for the difference of roots.
.
Now, we alrady know the sum and the product of the 2 roots. The formula which I have used is just to get the difference of the 2.

By the way , it might be a handy formula to remember.

Hope this helps.
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for a quadratic equation AX^2+BX+C = 0
SUM OF ROOTS = -B/A
PRODUCT OF ROOTS = C/A
let a AND b be the roots of equation
then a*b = C/A
a + b = -B/A

now as we have to calculate difference of roots (a-b)
we can use directly the formula (a-b)^2 = (a+b)^2 - 4ab...now simply you have to plug in the values..

hope it helps
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Hi Delsingh!
I looked through the discussion and decided to help you if you still need help
So have ever heard of Discriminant? This variable allows us to find roots of the equation without factoring. If you have a quadratic equation like a(x^2)+bx+c=0 then you can find Discriminant and roots. Formula for Discriminant is (b^2)-4ac. Formula for roots is x1=(-b+square root of Discriminant)/2a and for x2=(-b-square root of Discriminant)/2a. So you can find both roots and solve the problem. For example in our case Discriminant=25-4*(-12)*2=121. Hence x1=(-5+11)/4=1.5 and x2=(-5-11)/4=-4 Hope it is clear
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Roots are [-5 + sqrt(25 + 96)]/4 OR [-5 - sqrt(25 + 96)]/4
= 1.5 OR -4
Hence larger root 1.5 is 1.5 - (-4) = 5.5 = 11/2 greater than smaller root (-4).
Hence option (E).

--
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I do not think this question is from gmatprep.
pls show the picture

Solved in same way as above one.I personally feel that's the best approach rather than remembering any formula.

Hi all,

For those of you who wish to understand quadratics better or are already scrambled with formulas, I suggest to anyone that struggles with quadratics to go to this site (recommended by Bunuel): http://www.purplemath.com/modules/factquad.htm

The box method mentioned on the site makes questions like this cake.

In addition to that.

7. Algebra

• Theory
  Math : Algebra 101
  Algebra: Tips and hints
  FOIL on the GMAT: Simplifying and Expanding
  Factoring Quadratics
  Solving Quadratic Equations
  Using Algebra vs. Logic on GMAT Quant Questions
  
  • Questions
    Tough Algebra Set
    Algebra Ability Quiz by e-GMAT
    DS Questions
    PS Questions

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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I get the box method on that site, very helpful. But how do I use that to find how much the larger and smaller factors differ? It helps me get to (x+4)(2x-3) but I still don't know how much they differ? EDIT: nevermind.

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

Let the larger and smaller roots be l & s respectively

l + s = -5/2 = - 2.5
ls = -6

(l - s)^2 = 6.25 + 24 = 30.25 = 5.5^2
l - s = 5.5 = 11/2

IMO E
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\(2x^2+5x = 12\)
\(2x^2+5x-12 = 0\)

\(-12 * 2 = - 24\)
\((2x-3)(x+4)\)

\(x = 1.5, -4\)

Difference between -4 and 1.5 is 5.5.

\(5.5 = \frac{11}{2}\)
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\(2x^2+5x -12 = 0\)

Or, \(2x^2+8x - 3x -12 = 0\)

Or, \(2x( x + 4 ) - 3 ( x + 4) = 0\)

Or, \(x =\frac{3}{2}\) & \(x = -4\)

So , Larger root exceeds smaller root by \(\frac{3}{2} + 4 = \frac{11}{2}\), Answer must be (E)
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