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

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

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New post 22 Aug 2016, 04:15
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65% (01:30) correct 35% (02:06) wrong based on 161 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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Which of the following are roots of an equation x-2+2x-1-15=0 [#permalink]

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New post 22 Aug 2016, 05:15
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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:

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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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New post 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.
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Expert Post
Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
Posts: 5574
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GPA: 3.82
Re: Which of the following are roots of an equation x-2+2x-1-15=0 [#permalink]

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New post 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.

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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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New post 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
Re: Which of the following are roots of an equation x-2+2x-1-15=0   [#permalink] 04 Aug 2017, 14:05
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