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# What is the product of all the possible values of x if x^2(x + 2) + 7x

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Math Expert
Joined: 02 Sep 2009
Posts: 53792
What is the product of all the possible values of x if x^2(x + 2) + 7x  [#permalink]

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11 Dec 2015, 09:13
1
4
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Difficulty:

5% (low)

Question Stats:

83% (01:15) correct 17% (02:18) wrong based on 83 sessions

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What is the product of all the possible values of x if $$x^2(x + 2) + 7x(x + 2) + 6(x + 2) = 0$$?

A. –29
B. –12
C. 12
D. 29
E. 168

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Posts: 7431
Re: What is the product of all the possible values of x if x^2(x + 2) + 7x  [#permalink]

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11 Dec 2015, 09:39
1
Bunuel wrote:
What is the product of all the possible values of x if x^2(x + 2) + 7x(x + 2) + 6(x + 2) = 0?

A. –29
B. –12
C. 12
D. 29
E. 168

Hi,
the answer can be found in 10 secs, if you know the properties of the equations...
possible value of x means root of the equation..

the product of all roots= (-1)*highest power of x*the term without the variable(x here)/coeff of highest power of teh variable..
=-6*2/1=-12
B

edited the answer.. missed out on (-1)*highest power of x..
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Re: What is the product of all the possible values of x if x^2(x + 2) + 7x  [#permalink]

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12 Dec 2015, 00:13
2
chetan2u wrote:
Bunuel wrote:
What is the product of all the possible values of x if x^2(x + 2) + 7x(x + 2) + 6(x + 2) = 0?

A. –29
B. –12
C. 12
D. 29
E. 168

Hi,
the answer can be found in 10 secs, if you know the properties of the equations...
possible value of x means root of the equation..

the product of all roots=(-1)*highest power of x* the term without the variable(x here)/coeff of highest power of teh variable..
=-6*2/1=-12
B

By simple algebra, taking (x+2) common in the equation leaves,
$$(x+2)(x^2 + 7x + 6)$$ = 0
or (x+2)(x+1)(x+6) = 0.

This gives following possible values of x-
x = -2
x = -1
x = -6

So, the product of the three values = -12
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Re: What is the product of all the possible values of x if x^2(x + 2) + 7x  [#permalink]

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12 Dec 2015, 00:53
Bunuel,

Sorry if I may be the only one pointing out.

Can you write the question properly. On first sight, i thought x^2(x+2) meant the entire 2(x+2) was in the exponent position. After careful analysis, understood that its actually x^2 multiplied by (x+2).....
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Re: What is the product of all the possible values of x if x^2(x + 2) + 7x  [#permalink]

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12 Dec 2015, 08:29
FightToSurvive wrote:
Bunuel,

Sorry if I may be the only one pointing out.

Can you write the question properly. On first sight, i thought x^2(x+2) meant the entire 2(x+2) was in the exponent position. After careful analysis, understood that its actually x^2 multiplied by (x+2).....

_____________
Edited.
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What is the product of all the possible values of x if x^2(x + 2) + 7x  [#permalink]

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25 Apr 2016, 12:47
$$x^2(x+2)+7x(x+2)+6(x+2)=0$$
taking common factor of ( x + 2), we get
$$(x + 2) (x^2+7x +6)$$
(x+2)(x+1)(x+6)
taking roots we get x = -1,-2,-6
product of roots = -12
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What is the product of all the possible values of x if x^2(x + 2) + 7x  [#permalink]

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Updated on: 14 Aug 2016, 21:02
What is the product of all the possible values of x if x^2(x + 2) + 7x(x + 2) + 6(x + 2) = 0?

○○ –29
○○ –12
○○ 12
○○ 29
○○ 168

Originally posted by anurag7mukharya on 14 Aug 2016, 20:58.
Last edited by Vyshak on 14 Aug 2016, 21:02, edited 1 time in total.
Topic Merged
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Re: What is the product of all the possible values of x if x^2(x + 2) + 7x  [#permalink]

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15 Aug 2016, 03:05
x^2(x + 2) + 7x(x + 2) + 6(x + 2) = 0
=> (x+2)(x^2 + 7x + 6) = 0
=>(x+2)(x+1)(x+6)=0
=> x= -1 or -2 or -6
product =-12
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Re: What is the product of all the possible values of x if x^2(x + 2) + 7x  [#permalink]

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08 Mar 2019, 11:35
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Re: What is the product of all the possible values of x if x^2(x + 2) + 7x   [#permalink] 08 Mar 2019, 11:35
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