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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.
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.
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.
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 _________________
When you want to succeed as bad as you want to breathe ...then you will be successfull....
Re: Given that x^4 – 25x^2 = -144, which of the following is NOT [#permalink]
03 Jul 2013, 09:19
1
This post received KUDOS
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
Re: Given that x^4 – 25x^2 = -144, which of the following is NOT [#permalink]
24 Jul 2014, 07:14
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