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# What is the product of all the roots of the following equation?

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Manager
Status: Private GMAT Tutor
Joined: 22 Oct 2012
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Location: India
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What is the product of all the roots of the following equation? [#permalink]

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22 Aug 2017, 18:49
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25% (medium)

Question Stats:

82% (01:37) correct 18% (01:49) wrong based on 70 sessions

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What is the product of all the roots of the following equation?

$$x^5 - 3x^4 = 3x^2 - 3x^3 + 2x$$

A. 28
B. 19
C. 14
D. 1
E. 0
[Reveal] Spoiler: OA

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Last edited by ChiranjeevSingh on 22 Aug 2017, 20:00, edited 5 times in total.

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Math Expert
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Posts: 5526

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What is the product of all the roots of the following equation? [#permalink]

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22 Aug 2017, 19:14
1
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Expert's post
ChiranjeevSingh wrote:
What is the product of all the roots of the following equation?

$$x^5 - 3x^4 = 3x^2 - 3x^3 + 2x$$

A. 28
B. 14
C. 19
D. 0
E. 1

I'll post the OA in a while!

Hi..

X is common to all terms so one value of x is 0..
No need to go any further..
Product of all terms with one of them as 0 will be 0
E
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Math Expert
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Re: What is the product of all the roots of the following equation? [#permalink]

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22 Aug 2017, 19:55
1
KUDOS
Expert's post
ChiranjeevSingh wrote:
What is the product of all the roots of the following equation?

$$x^5 - 3x^4 = 3x^2 - 3x^3 + 2x$$

A. 28
B. 14
C. 19
D. 0
E. 1

I'll post the OA in a while!

You have to post the OA from the beginning. Also, on the GMAT, answer choices are in ascending or descending order.
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Concentration: Strategy, Technology
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Re: What is the product of all the roots of the following equation? [#permalink]

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22 Aug 2017, 22:31
ChiranjeevSingh wrote:
What is the product of all the roots of the following equation?

$$x^5 - 3x^4 = 3x^2 - 3x^3 + 2x$$

A. 28
B. 19
C. 14
D. 1
E. 0

since equation becomes
$$x(x^4-3x^3+3x^2-3x-2)=0$$
one of the roots will be x=0

Hence product of all roots will be 0
E
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Re: What is the product of all the roots of the following equation? [#permalink]

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23 Aug 2017, 02:07
Taking x common and all the terms on left side ,
x(x4−3x3+3x2−3x−2)=0
Which equuals ,

x=0 or x4-3x3=3x2-2=0

One of the root is 0 . That means product of roots = 0

Kudos [?]: 1 [0], given: 1

Re: What is the product of all the roots of the following equation?   [#permalink] 23 Aug 2017, 02:07
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