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# Find the arithmetic mean of all roots of the following equation

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Intern
Joined: 05 Apr 2011
Posts: 10
Find the arithmetic mean of all roots of the following equation  [#permalink]

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Updated on: 14 Dec 2016, 23:26
3
8
00:00

Difficulty:

25% (medium)

Question Stats:

73% (01:29) correct 27% (01:41) wrong based on 211 sessions

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Find the arithmetic mean of all roots of the following equation

$$(x+2) \sqrt{x-x^2}=0$$

A) 2
B) 1
C) 0.5
D) -1/3
E) 0.3

Originally posted by SteveNew on 25 May 2011, 13:38.
Last edited by Bunuel on 14 Dec 2016, 23:26, edited 5 times in total.
Renamed the topic.
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Re: Find the arithmetic mean of all roots of the following equation  [#permalink]

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25 May 2011, 18:36
SteveNew wrote:
Hello Guys,

Find the arithmetic mean of all roots of the following equation- see an attachment.

A 2
B 1
C 0.5
D -1/3
E 0.5

Thanks,
Steve.

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Posts: 10
Re: Find the arithmetic mean of all roots of the following equation  [#permalink]

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25 May 2011, 18:45
Thank you so much Agdimple,

It was corrected.

Steve.
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Re: Find the arithmetic mean of all roots of the following equation  [#permalink]

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25 May 2011, 23:18
1
I am getting D.

Equation is $$(x+2) \sqrt{x-x^2}=0$$
x+2=0 or x=-2
$$\sqrt{x-x^2}=0$$
x-x^2=0
x(1-x)=0
or x=0
or x=1

Average of all roots= -2+0+1/3=-1/3.
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Re: Find the arithmetic mean of all roots of the following equation  [#permalink]

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25 May 2011, 23:38
the solutions are x = -2,0 and 1
the mean = -1/3.
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Re: Find the arithmetic mean of all roots of the following equation  [#permalink]

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14 Dec 2016, 14:54
1
Excellent Official Questions.
Here is my solution to this one =>
The roots of the equation will be => {-2,0,1}

Hence the mean => $$\frac{-2+0+1}{3} => \frac{-1}{3}$$
Hence D
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Re: Find the arithmetic mean of all roots of the following equation  [#permalink]

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22 Mar 2019, 17:12
Just to know, is there a possibility o create an eq multiplying both terms?
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Re: Find the arithmetic mean of all roots of the following equation  [#permalink]

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23 Mar 2019, 06:19
2
SteveNew wrote:
Find the arithmetic mean of all roots of the following equation

$$(x+2) \sqrt{x-x^2}=0$$

A) 2
B) 1
C) 0.5
D) -1/3
E) 0.3

Why is -2 considered a solution? the square root of a negative number doesn't exist, if you plugg in back in the equation this is impossible...
Hence, only possible solutions are 0 and 1; so C

Can someone help?
Re: Find the arithmetic mean of all roots of the following equation   [#permalink] 23 Mar 2019, 06:19
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