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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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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 Updated on: 12 Nov 2019, 18:21
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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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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.
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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 26 Feb 2019, 07:26
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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

Answer:

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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.

Start with: 15x² - 2x - 1 = 0
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.
So, we can start with: (__ + 1)(__ - 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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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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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
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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 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

Answer:

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Hello GMATPrepNow !

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

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

Viete's theorem

Addition:

\(\frac{-b}{a}\)

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


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

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New post 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.
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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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