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Which of the following are roots of an equation (x^-2)+(2x^-

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Which of the following are roots of an equation (x^-2)+(2x^-

by Max@Math Revolution » Mon Aug 22, 2016 3:15 am
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

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by Brent@GMATPrepNow » Mon Aug 22, 2016 4:17 am
Max@Math Revolution 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: B
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by Max@Math Revolution » Wed Aug 24, 2016 4:38 am
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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