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Given that x^4 – 25x^2 = -144, which of the following is NOT

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subhashghosh
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Given that x^4 – 25x^2 = -144, which of the following is NOT [#permalink] New post   Updated on: 03 May 2013, 03:14
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Given that x^4 – 25x^2 = -144, which of the following is NOT a sum of two possible values of x?

A. -7
B. -1
C. 0
D. 3
E. 7
ShowHide Answer
Official Answer
D

Originally posted by subhashghosh on 30 Jan 2011, 04:38.
Last edited by Bunuel on 03 May 2013, 03:14, edited 2 times in total.
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Bunuel
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Re: MGMAT Challenge question doubt [#permalink] New post   30 Jan 2011, 06:23
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subhashghosh wrote:
Hi

I have a doubt in this question :

Given that x^4 - 25x^2 = -144 , which of the following is NOT a sum of two possible values of x ?

Official Answer - D

The roots are x = 4 or -4, and -3 or +3

These values are considered for the sum,

-7 = -4+ -3

-1 = -4 + 3

0 = -4 + 4 or -3 + 3

7 = 4 + 3

But why was 4 -3 not considered ?

Regards,
Subhash


Subhash, please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html

So please:
Provide answer choices for PS questions.

Original question is:
Given that x^4 – 25x^2 = -144, which of the following is NOT a sum of two possible values of x?
A. -7
B. -1
C. 0
D. 3
E. 7

Factor \(x^4-25x^2+144=0\) --> \((x^2 - 16)*(x^2 - 9)=0\) --> \(x^2=16\) or \(x^2=9\) (alternately you could solve \(x^4-25x^2+144=0\) for \(x^2\) to get the same values for it) --> \(x=4\) or \(x=-4\) or \(x=3\) or \(x=-3\).

All but option D. could be expressed as the sum of two roots: A. 7=-4-3; B. -1=-3+4; C. 0=3-3 (or 0=4-4); E. 7=3+4.

Answer: D.

As for your question: there are no enough answer choices to show all possible values of a sum of two roots, so there are 4 possible values for a sum and one which is not.

Hope it's clear.
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Re: MGMAT Challenge question doubt [#permalink] New post   01 May 2013, 05:07
Bunuel wrote:
subhashghosh wrote:
Hi

I have a doubt in this question :

Given that x^4 - 25x^2 = -144 , which of the following is NOT a sum of two possible values of x ?

Official Answer - D

The roots are x = 4 or -4, and -3 or +3

These values are considered for the sum,

-7 = -4+ -3

-1 = -4 + 3

0 = -4 + 4 or -3 + 3

7 = 4 + 3

But why was 4 -3 not considered ?

Regards,
Subhash


Subhash, please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html

So please:
Provide answer choices for PS questions.

Original question is:
Given that x^4 – 25x^2 = -144, which of the following is NOT a sum of two possible values of x?
A. -7
B. -1
C. 0
D. 3
E. 7

Factor \(x^4-25x^2+144=0\) --> \((x^2 - 16)*(x^2 - 9)=0\) --> \(x^2=16\) or \(x^2=9\) (alternately you could solve \(x^4-25x^2+144=0\) for \(x^2\) to get the same values for it) --> \(x=4\) or \(x=-4\) or \(x=3\) or \(x=-3\).

All but option D. could be expressed as the sum of two roots: A. 7=-4-3; B. -1=-3+4; C. 0=3-3 (or 0=4-4); E. 7=3+4.

Answer: D.

As for your question: there are no enough answer choices to show all possible values of a sum of two roots, so there are 4 possible values for a sum and one which is not.

Hope it's clear.


How did u calculate the highlighted part.
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Bunuel
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Re: MGMAT Challenge question doubt [#permalink] New post   01 May 2013, 05:20
Expert Reply
Rajkiranmareedu wrote:
Bunuel wrote:
subhashghosh wrote:
Hi

I have a doubt in this question :

Given that x^4 - 25x^2 = -144 , which of the following is NOT a sum of two possible values of x ?

Official Answer - D

The roots are x = 4 or -4, and -3 or +3

These values are considered for the sum,

-7 = -4+ -3

-1 = -4 + 3

0 = -4 + 4 or -3 + 3

7 = 4 + 3

But why was 4 -3 not considered ?

Regards,
Subhash


Subhash, please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html

So please:
Provide answer choices for PS questions.

Original question is:
Given that x^4 – 25x^2 = -144, which of the following is NOT a sum of two possible values of x?
A. -7
B. -1
C. 0
D. 3
E. 7

Factor \(x^4-25x^2+144=0\) --> \((x^2 - 16)*(x^2 - 9)=0\) --> \(x^2=16\) or \(x^2=9\) (alternately you could solve \(x^4-25x^2+144=0\) for \(x^2\) to get the same values for it) --> \(x=4\) or \(x=-4\) or \(x=3\) or \(x=-3\).

All but option D. could be expressed as the sum of two roots: A. 7=-4-3; B. -1=-3+4; C. 0=3-3 (or 0=4-4); E. 7=3+4.

Answer: D.

As for your question: there are no enough answer choices to show all possible values of a sum of two roots, so there are 4 possible values for a sum and one which is not.

Hope it's clear.


How did u calculate the highlighted part.


Solving and Factoring Quadratics:
https://www.purplemath.com/modules/solvquad.htm
https://www.purplemath.com/modules/factquad.htm

Hope it helps.
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Re: MGMAT Challenge question doubt [#permalink] New post   03 May 2013, 01:38
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Rajkiranmareedu wrote:
Bunuel wrote:
subhashghosh wrote:
Hi

I have a doubt in this question :

Given that x^4 - 25x^2 = -144 , which of the following is NOT a sum of two possible values of x ?

Official Answer - D

The roots are x = 4 or -4, and -3 or +3

These values are considered for the sum,

-7 = -4+ -3

-1 = -4 + 3

0 = -4 + 4 or -3 + 3

7 = 4 + 3

But why was 4 -3 not considered ?

Regards,
Subhash


Subhash, please read and follow: how-to-improve-the-forum-search-function-for-others-99451.html

So please:
Provide answer choices for PS questions.

Original question is:
Given that x^4 – 25x^2 = -144, which of the following is NOT a sum of two possible values of x?
A. -7
B. -1
C. 0
D. 3
E. 7

Factor \(x^4-25x^2+144=0\) --> \((x^2 - 16)*(x^2 - 9)=0\) --> \(x^2=16\) or \(x^2=9\) (alternately you could solve \(x^4-25x^2+144=0\) for \(x^2\) to get the same values for it) --> \(x=4\) or \(x=-4\) or \(x=3\) or \(x=-3\).

All but option D. could be expressed as the sum of two roots: A. 7=-4-3; B. -1=-3+4; C. 0=3-3 (or 0=4-4); E. 7=3+4.

Answer: D.

As for your question: there are no enough answer choices to show all possible values of a sum of two roots, so there are 4 possible values for a sum and one which is not.

Hope it's clear.


How did u calculate the highlighted part.


To calculate the roots of a quadratic equation ax^2+bx+c=0
you can use the formula
roots =(-b+sqrt(b^2-4ac))/2a...and .....(-b-sqrt(b^2-4ac))/2a

now in this x^4-25x^2+144=0===>just for convenience put x^2= X
therefore equation becomes: X^2-25X+144=0

NOW using the formula of roots

X=(25+sqrt(25^2-4*1*144))/2 and X=(25-sqrt(25^2-4*1*144))/2
On simplifying
X=16...AND X=9
now replacing back X WITH x
we get x^2=16 and x^2=9
therefore four roots are x=+4,-4,+3,-3

hope it helps...

SKM

hope it h
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Re: Given that x^4 – 25x^2 = -144, which of the following is NOT [#permalink] New post   03 Jul 2013, 01:23
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

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Re: Given that x^4 – 25x^2 = -144, which of the following is NOT [#permalink] New post   03 Jul 2013, 10:19
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subhashghosh wrote:
Given that x^4 – 25x^2 = -144, which of the following is NOT a sum of two possible values of x?

A. -7
B. -1
C. 0
D. 3
E. 7




Factorization of roots initially conisder 144 and now diivide this to roots which add to 25 => 16, 9
and now
x^2 -9 and x^2 -15 one of them is equal to zero, equate and we get l3l l4l as the roots
so add them individually in all combniations we can achieve all othe but not 3 as sum of two roots

so the answer is D

hope this helps
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Re: Given that x^4 – 25x^2 = -144, which of the following is NOT [#permalink] New post   03 Jul 2013, 13:50
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Assume, \(x ^2 = y\); then the equation is \(y^2 -25y+144=0\)

sum of the roots = 25 = y1 + y2

product of the roots = \(144 = y1 * y2\)

==> y1 - y2 = 7

==> y1 = 16 and y2 = 9

==> \(x^2\) = 16, 9

==> x = +4, -4, +3 , -3

so sum of any two values of x is not '3'
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Re: Given that x^4 25x^2 = -144, which of the following is NOT [#permalink] New post   30 Jun 2023, 11:55
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Re: Given that x^4 25x^2 = -144, which of the following is NOT [#permalink]
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