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# Which of the following are roots of an equation x-2+2x-1-15=0

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Math Revolution GMAT Instructor
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Which of the following are roots of an equation x-2+2x-1-15=0  [#permalink]

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22 Aug 2016, 04:15
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55% (hard)

Question Stats:

66% (02:05) correct 34% (02:17) wrong based on 221 sessions

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Which of the following are roots of an equation (x^-2)+(2x^-1)-15=0
A. 1/5 and -1/3
B. -1/5 and 1/3
C. 1/5 and 1/3
D. -1/5 and -1/3
E. -5/2 and -1/3

*An answer will be posted in 2 days.

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMAT Club Legend Joined: 12 Sep 2015 Posts: 4068 Location: Canada Which of the following are roots of an equation x-2+2x-1-15=0 [#permalink] ### Show Tags Updated on: 12 Nov 2019, 18:21 3 Top Contributor 1 MathRevolution wrote: Which of the following are roots of an equation (x^-2)+(2x^-1)-15=0 A. 1/5 and -1/3 B. -1/5 and 1/3 C. 1/5 and 1/3 D. -1/5 and -1/3 E. -5/2 and -1/3 Given: (x^-2) + (2x^-1) - 15 = 0 Rewrite as: 1/(x²) + 2/x - 15 = 0 Remove fractions by multiplying both sides by x² to get: 1 + 2x - 15x² = 0 Rearrange to get: 15x² - 2x - 1 = 0 Factor to get: (5x + 1)(3x - 1) = 0 So, EITHER 5x + 1 OR 3x - 1 = 0 If 5x + 1 = 0, then x = -1/5 If 3x - 1 = 0, then x = 1/3 So, the roots (solutions) are -1/5 and 1/3 Answer: _________________ Test confidently with gmatprepnow.com Originally posted by GMATPrepNow on 22 Aug 2016, 05:15. Last edited by GMATPrepNow on 12 Nov 2019, 18:21, edited 1 time in total. Board of Directors Status: Stepping into my 10 years long dream Joined: 18 Jul 2015 Posts: 3568 Re: Which of the following are roots of an equation x-2+2x-1-15=0 [#permalink] ### Show Tags 22 Aug 2016, 10:44 MathRevolution wrote: Which of the following are roots of an equation (x^-2)+(2x^-1)-15=0 A. 1/5 and -1/3 B. -1/5 and 1/3 C. 1/5 and 1/3 D. -1/5 and -1/3 E. -5/2 and -1/3 *An answer will be posted in 2 days. 2 ways to solve this question : 1) Take x^-1 = y and solve the equation y^2 + 2y - 15=0; 2) Substitute the value of x from options and check which one satisfy. _________________ My LinkedIn abhimahna. My GMAT Story: From V21 to V40 My MBA Journey: My 10 years long MBA Dream My Secret Hacks: Best way to use GMATClub | Importance of an Error Log! Verbal Resources: All SC Resources at one place | All CR Resources at one place GMAT Club Inbuilt Error Log Functionality - View More. New Visa Forum - Ask all your Visa Related Questions - here. New! Best Reply Functionality on GMAT Club! Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free Check our new About Us Page here. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8152 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: Which of the following are roots of an equation x-2+2x-1-15=0 [#permalink] ### Show Tags 24 Aug 2016, 05:38 If we multiply both sides by x^2, we get 1+2x-15x^2=0, (15x^2)-2x-1=0, (3x-1)(5x+1)=0. Hence, x=1/3 or -1/5, and the correct answer is B. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: Which of the following are roots of an equation x-2+2x-1-15=0  [#permalink]

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04 Aug 2017, 14:05
Hi,

I have two questions related to answers

1. How 15x² - 2x - 1 = 0 get: (5x + 1)(3x - 1) = 0 . I get 1 X -1 = -1 ok, but 1+(-1) = 0 NOT 2.

2. Is there a rule to put the values into the ()? . I could have 15x² - 2x - 1 = 0 to get: (5x - 1)(3x + 1) in this case the answer is A

Thanks
Senior Manager
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Re: Which of the following are roots of an equation x-2+2x-1-15=0  [#permalink]

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25 Feb 2019, 18:55
GMATPrepNow wrote:
MathRevolution wrote:
Which of the following are roots of an equation (x^-2)+(2x^-1)-15=0

A. 1/5 and -1/3
B. -1/5 and 1/3
C. 1/5 and 1/3
D. -1/5 and -1/3
E. -5/2 and -1/3

Given: (x^-2) + (2x^-1) - 15 = 0
Rewrite as: 1/(x²) + 2/x - 15 = 0
Remove fractions by multiplying both sides by x² to get: 1 + 2x - 15x² = 0
Rearrange to get: 15x² - 2x - 1 = 0
Factor to get: (5x + 1)(3x - 1) = 0
So, EITHER 5x + 1 OR 3x - 1 = 0
If 5x + 1 = 0, then x = -1/5
If 3x - 1 = 0, then x = 1/3

So, the roots (solutions) are -1/5 and 1/3

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Hello GMATPrepNow !

Would you mind to explain how do you factorize the "red term"?

Kind regards!
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 4068
Re: Which of the following are roots of an equation x-2+2x-1-15=0  [#permalink]

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26 Feb 2019, 07:26
1
Top Contributor
jfranciscocuencag wrote:
GMATPrepNow wrote:
MathRevolution wrote:
Which of the following are roots of an equation (x^-2)+(2x^-1)-15=0

A. 1/5 and -1/3
B. -1/5 and 1/3
C. 1/5 and 1/3
D. -1/5 and -1/3
E. -5/2 and -1/3

Given: (x^-2) + (2x^-1) - 15 = 0
Rewrite as: 1/(x²) + 2/x - 15 = 0
Remove fractions by multiplying both sides by x² to get: 1 + 2x - 15x² = 0
Rearrange to get: 15x² - 2x - 1 = 0
Factor to get: (5x + 1)(3x - 1) = 0
So, EITHER 5x + 1 OR 3x - 1 = 0
If 5x + 1 = 0, then x = -1/5
If 3x - 1 = 0, then x = 1/3

So, the roots (solutions) are -1/5 and 1/3

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Hello GMATPrepNow !

Would you mind to explain how do you factorize the "red term"?

Kind regards!

This factorization can be performed with a little intuitive testing.

Since the last term is -1, we know that the constant terms in the 2 binomials must have a product of -1. So, the first two terms must be +1 and -1.
We also know that the first terms in the 2 binomials must have a product of 15x²
So, the first two terms must be either 3x and 5x or 15x and x

Let's test 3x and 5x first.
We get (3x + 1)(5x - 1) = 0
To see if this factorization is correct, expand and simplify to get: 15x² + 2x - 1 = 0
VERY CLOSE!! We want 15x² - 2x - 1 = 0

So, let's SWITCH the 3x and 5x to get: (5x + 1)(3x - 1) = 0
To see if this factorization is correct, expand and simplify to get: 15x² - 2x - 1 = 0 PERFECT

Does that help?

Cheers,
Brent
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Which of the following are roots of an equation x-2+2x-1-15=0  [#permalink]

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07 Mar 2019, 20:24
I found another solution that may help others who are not so good factorizing like me:

Viete's theorem

$$\frac{-b}{a}$$

$$\frac{-(-2)}{15}$$ = $$\frac{2}{15}$$

Multiplication:

$$\frac{-1}{15}$$

Now just do some testing with the results, you are looking for $$\frac{-1}{15}$$ if you multiply the options or $$\frac{2}{15}$$ if you like to add.

Hence,

B. -1/5 and 1/3

$$\frac{-1}{5}*\frac{1}{3}$$ = $$\frac{-1}{15}$$

B
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Joined: 13 Jul 2019
Posts: 2
Re: Which of the following are roots of an equation x-2+2x-1-15=0  [#permalink]

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07 Oct 2019, 07:38
Hi,

I arrived at the correct answer by pretending that the negative exponents were not there. Did I just get lucky?

x^2 - 2x - 15 = 0 --> (x+5)(x-3)

Then I checked the answer choices, that listed the first option as a negative number with a 5 on it and positive number with 3 on it.
Re: Which of the following are roots of an equation x-2+2x-1-15=0   [#permalink] 07 Oct 2019, 07:38
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