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# For how many real values of x is this expression equal to zero?

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Manager
Joined: 13 May 2017
Posts: 107
Location: Finland
Concentration: Accounting, Entrepreneurship
GMAT 1: 530 Q42 V22
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WE: Account Management (Entertainment and Sports)
For how many real values of x is this expression equal to zero?  [#permalink]

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21 Nov 2018, 08:17
4
00:00

Difficulty:

65% (hard)

Question Stats:

42% (01:13) correct 58% (01:11) wrong based on 52 sessions

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For how many real values of x is this expression equal to zero?

$$\frac{x^3−x^2−6x}{(4−x^2)^2}$$

A. 0
B. 1
C. 2
D. 3
E. 4
Intern
Joined: 15 Nov 2018
Posts: 13
Re: For how many real values of x is this expression equal to zero?  [#permalink]

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21 Nov 2018, 08:26
For this question, we can ignore the denominator, for it cannot be zero, and focus on values that yield '0' in the numerator.

x^3-x^2-6x can be simplified to:

x(x^2-x-6)
x(x+2)(x-3)

which gives us two real values (-2) and (3) that will result in '0' in the numerator.

the answer is [C] I believe
Senior Manager
Joined: 09 Aug 2017
Posts: 333
Re: For how many real values of x is this expression equal to zero?  [#permalink]

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21 Nov 2018, 08:50
1
Numerator can be zero for 3 values.
0, -2, 3
but for x=-2 denominator will be zero, which will yield 0/0 that is not desirable.
So only two values of x are acceptable here.
C is correct choice.
Intern
Joined: 02 Jun 2018
Posts: 15
Location: India
Concentration: Finance
GPA: 4
Re: For how many real values of x is this expression equal to zero?  [#permalink]

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27 Nov 2018, 00:29
gvij2017 wrote:
Numerator can be zero for 3 values.
0, -2, 3
but for x=-2 denominator will be zero, which will yield 0/0 that is not desirable.
So only two values of x are acceptable here.
C is correct choice.

Why is 0/0 not desirable if the question asks for the expression to be 0 ?
Intern
Joined: 20 Aug 2017
Posts: 27
Re: For how many real values of x is this expression equal to zero?  [#permalink]

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27 Nov 2018, 03:39
1
shobhiitgupta wrote:
gvij2017 wrote:
Numerator can be zero for 3 values.
0, -2, 3
but for x=-2 denominator will be zero, which will yield 0/0 that is not desirable.
So only two values of x are acceptable here.
C is correct choice.

Why is 0/0 not desirable if the question asks for the expression to be 0 ?

Because anything divided by 0 does not results to 0 rather its undefined.
Re: For how many real values of x is this expression equal to zero?   [#permalink] 27 Nov 2018, 03:39
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