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What is the average (arithmetic mean) of all solutions to the equation

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What is the average (arithmetic mean) of all solutions to the equation [#permalink]

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New post 14 Feb 2017, 02:03
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Re: What is the average (arithmetic mean) of all solutions to the equation [#permalink]

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New post 14 Feb 2017, 03:06
Bunuel wrote:
What is the average (arithmetic mean) of all solutions to the equation \(x^3 − 2x^2 − 8x = 0\)?

A. −2
B. −2/3
C. 2/3
D. 2
E. 8/3


Hi

\(x^3 − 2x^2 − 8x = 0\)==>x\((x^2-2x-8)\)==>x(x-4)(x+2)=0

Sum of all solution =0-2+4=2

Average=2/3

Hence C
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Re: What is the average (arithmetic mean) of all solutions to the equation [#permalink]

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New post 14 Feb 2017, 04:38
sum of all roots is 2..so 2/3

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Re: What is the average (arithmetic mean) of all solutions to the equation [#permalink]

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New post 14 Feb 2017, 06:01
0, 4, -2 are the roots of the given equation.

Average = (0 + 4 -2)/3 = 2/3

Option C
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Re: What is the average (arithmetic mean) of all solutions to the equation [#permalink]

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New post 14 Feb 2017, 08:19
Bunuel wrote:
What is the average (arithmetic mean) of all solutions to the equation \(x^3 − 2x^2 − 8x = 0\)?

A. −2
B. −2/3
C. 2/3
D. 2
E. 8/3


\(x^3 − 2x^2 − 8x = 0\)

Or, \(x(x^2 − 2x − 8) = 0\)

Or, Either \(x = 0\) or \(x^2 − 2x − 8 = 0\)

If, \(x^2 − 2x − 8 = 0\)

Or, \(x^2 − 4x + 2x − 8 = 0\)

Or, \(x ( x − 4 ) +2 ( x − 4 ) = 0\)

Or, \(x = -2\) or , \(x = 4\)

Here we have three values of x as :

(1) x = 0
(2) x = -2
(3) x = 4

Average will be \(\frac{( 0 + 4 - 2 )}{3} = \frac{2}{3}\)

Hence, answer will be (C) \(\frac{2}{3}\)
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Re: What is the average (arithmetic mean) of all solutions to the equation [#permalink]

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New post 15 Feb 2017, 16:16
Bunuel wrote:
What is the average (arithmetic mean) of all solutions to the equation \(x^3 − 2x^2 − 8x = 0\)?

A. −2
B. −2/3
C. 2/3
D. 2
E. 8/3


We can simplify the given equation, first by factoring out the common x from each term:

x^3 - 2x^2 - 8x = 0

x(x^2 - 2x - 8) = 0

Now factor the expression in the parentheses:

x(x - 4)(x + 2) = 0

x = 0 or x = 4 or x = -2

The average of these terms is (0 + 4 + (-2))/3 = ⅔.

Answer: C
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Re: What is the average (arithmetic mean) of all solutions to the equation   [#permalink] 15 Feb 2017, 16:16
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