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# By how much does the larger root of the equation 2x^2+5x = 1

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Manager
Joined: 25 Jul 2012
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By how much does the larger root of the equation 2x^2+5x = 1  [#permalink]

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04 Aug 2013, 10:50
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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

Source: GMATPrep Question Pack 1
Difficulty: Hard
------------
The problem I was having with this question was factoring out

2x^2 + 5x -12 = 0

How do I factor the equation when the x^2 has a coefficient that's not 1 -- in this case 2?

Thanks

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Re: By how much does the larger root of the equation 2x^2+5x = 1  [#permalink]

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02 Apr 2015, 12:22
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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

GMAT assassins aren't born, they're made,
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# Rich Cohen

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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** ##### Most Helpful Community Reply SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1829 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) By how much does the larger root of the equation 2x^2+5x = 1 [#permalink] ### Show Tags Updated on: 03 Nov 2014, 01:23 5 5 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) _________________ Kindly press "+1 Kudos" to appreciate Originally posted by PareshGmat on 31 Oct 2013, 01:25. Last edited by PareshGmat on 03 Nov 2014, 01:23, edited 1 time in total. ##### General Discussion Verbal Forum Moderator Joined: 10 Oct 2012 Posts: 613 Re: By how much does the larger root of the equation 2x^2+5x = 1 [#permalink] ### Show Tags 04 Aug 2013, 11:00 4 3 DelSingh 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 Source: GMATPrep Question Pack 1 Difficulty: Hard ------------ The problem I was having with this question was factoring out 2x^2 + 5x -12 = 0 How do I factor the equation when the x^2 has a coefficient that's not 1 -- in this case 2? Thanks 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. _________________ Director Joined: 14 Dec 2012 Posts: 771 Location: India Concentration: General Management, Operations GMAT 1: 700 Q50 V34 GPA: 3.6 Re: By how much does the larger root of the equation 2x^2+5x = 1 [#permalink] ### Show Tags 04 Aug 2013, 11:00 2 DelSingh 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 Source: GMATPrep Question Pack 1 Difficulty: Hard ------------ The problem I was having with this question was factoring out 2x^2 + 5x -12 = 0 How do I factor the equation when the x^2 has a coefficient that's not 1 -- in this case 2? Thanks 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 _________________ When you want to succeed as bad as you want to breathe ...then you will be successfull.... GIVE VALUE TO OFFICIAL QUESTIONS... GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabulary-list-for-gmat-reading-comprehension-155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment : http://www.youtube.com/watch?v=APt9ITygGss Manager Joined: 25 Jul 2012 Posts: 68 Location: United States Re: By how much does the larger root of the equation 2x^2+5x = 1 [#permalink] ### Show Tags 04 Aug 2013, 11:27 1 mau5 wrote: DelSingh 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 Source: GMATPrep Question Pack 1 Difficulty: Hard ------------ The problem I was having with this question was factoring out 2x^2 + 5x -12 = 0 How do I factor the equation when the x^2 has a coefficient that's not 1 -- in this case 2? Thanks 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. Note that $$(a-b)^2 = (a+b)^2-4ab$$ How are you getting this? I thought $$(a-b)^2 = a^2 -2ab+ b^2$$ _________________ If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^ Verbal Forum Moderator Joined: 10 Oct 2012 Posts: 613 Re: By how much does the larger root of the equation 2x^2+5x = 1 [#permalink] ### Show Tags 04 Aug 2013, 11:30 DelSingh wrote: mau5 wrote: DelSingh 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 Source: GMATPrep Question Pack 1 Difficulty: Hard ------------ The problem I was having with this question was factoring out 2x^2 + 5x -12 = 0 How do I factor the equation when the x^2 has a coefficient that's not 1 -- in this case 2? Thanks 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. 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. _________________ Manager Joined: 25 Jul 2012 Posts: 68 Location: United States Re: By how much does the larger root of the equation 2x^2+5x = 1 [#permalink] ### Show Tags 04 Aug 2013, 11:57 mau5 wrote: 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. 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. $$(a+b)^2-4ab = a^2+b^2+2ab-4ab = a^2 -2ab+ b^2$$ 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 _________________ If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^ Verbal Forum Moderator Joined: 10 Oct 2012 Posts: 613 Re: By how much does the larger root of the equation 2x^2+5x = 1 [#permalink] ### Show Tags 04 Aug 2013, 12:06 DelSingh wrote: mau5 wrote: 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. 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. $$(a+b)^2-4ab = a^2+b^2+2ab-4ab = a^2 -2ab+ b^2$$ 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. _________________ Director Joined: 14 Dec 2012 Posts: 771 Location: India Concentration: General Management, Operations GMAT 1: 700 Q50 V34 GPA: 3.6 Re: By how much does the larger root of the equation 2x^2+5x = 1 [#permalink] ### Show Tags 04 Aug 2013, 12:07 2 1 DelSingh wrote: mau5 wrote: 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. 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. $$(a+b)^2-4ab = a^2+b^2+2ab-4ab = a^2 -2ab+ b^2$$ 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 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 _________________ When you want to succeed as bad as you want to breathe ...then you will be successfull.... GIVE VALUE TO OFFICIAL QUESTIONS... GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabulary-list-for-gmat-reading-comprehension-155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment : http://www.youtube.com/watch?v=APt9ITygGss Senior Manager Joined: 02 Dec 2014 Posts: 387 Location: Russian Federation Concentration: General Management, Economics GMAT 1: 640 Q44 V33 WE: Sales (Telecommunications) Re: By how much does the larger root of the equation 2x^2+5x = 1 [#permalink] ### Show Tags 31 Mar 2015, 05:20 DelSingh wrote: mau5 wrote: 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. 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. $$(a+b)^2-4ab = a^2+b^2+2ab-4ab = a^2 -2ab+ b^2$$ 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 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 _________________ "Are you gangsters?" - "No we are Russians!" SVP Joined: 06 Nov 2014 Posts: 1883 Re: By how much does the larger root of the equation 2x^2+5x = 1 [#permalink] ### Show Tags 31 Mar 2015, 11:54 DelSingh 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 Source: GMATPrep Question Pack 1 Difficulty: Hard ------------ The problem I was having with this question was factoring out 2x^2 + 5x -12 = 0 How do I factor the equation when the x^2 has a coefficient that's not 1 -- in this case 2? Thanks 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). -- Optimus Prep's GMAT On Demand course for only$299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimus-prep.com/gmat-on-demand-course
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Re: By how much does the larger root of the equation 2x^2+5x = 1  [#permalink]

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02 Apr 2015, 00:37
I do not think this question is from gmatprep.
pls show the picture
Intern
Joined: 14 May 2017
Posts: 49
Re: By how much does the larger root of the equation 2x^2+5x = 1  [#permalink]

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16 Nov 2017, 18:08
PareshGmat wrote:
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)

Solved in same way as above one.I personally feel that's the best approach rather than remembering any formula.
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Re: By how much does the larger root of the equation 2x^2+5x = 1  [#permalink]

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01 Mar 2018, 23:07
1
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.
Math Expert
Joined: 02 Sep 2009
Posts: 49992
Re: By how much does the larger root of the equation 2x^2+5x = 1  [#permalink]

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01 Mar 2018, 23:14
mrosale2 wrote:
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.

7. Algebra

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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By how much does the larger root of the equation 2x^2+5x = 1  [#permalink]

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25 Jul 2018, 14:02
mrosale2 wrote:
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.

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.
By how much does the larger root of the equation 2x^2+5x = 1 &nbs [#permalink] 25 Jul 2018, 14:02
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