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5 roots in one equation

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ghentu
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5 roots in one equation [#permalink] New post   14 Jan 2010, 05:31
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D
E

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If a, b, c, d and e are the five positive roots of the equation x5 − 5x^4 + kx^3 + mx^2 + nx − 1 = 0

How to find sum of products of 2 roots taken at a time ?

How to find sum of products of 3 roots taken at a time ?


I want to derive .... not from memory mug up



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Re: 5 roots in one equation [#permalink] New post   14 Jan 2010, 08:43
ghentu wrote:
If a, b, c, d and e are the five positive roots of the equation x5 − 5x^4 + kx^3 + mx^2 + nx − 1 = 0

How to find sum of products of 2 roots taken at a time ?

How to find sum of products of 3 roots taken at a time ?


I want to derive .... not from memory mug up


I believe quadratic equations are the largest power of a variable applicable for GMAT level questions. We don't even need to know (a+b)^3 formula.
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testprep2010
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Re: 5 roots in one equation [#permalink] New post   12 Feb 2010, 21:52
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(x-a)(x-b)(x-c)(x-d)(x-e)
= x^5
- (a+b+c+d+e) x^4 --[one at a time]
+ (ab+ac+ad+ae+bc+db+be+cd+ce+de...2 at a time) x^3
- (abc+acd+ade+bcd+bce+cde...3 at a time) x^2
+ (abcd+acde+abde+...4 at a time) x
- abcde

x5 − 5x^4 + kx^3 + mx^2 + nx − 1 = 0

How to find sum of products of 2 roots taken at a time ? k

How to find sum of products of 3 roots taken at a time ? -m


Hope this helps!
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Re: 5 roots in one equation [#permalink] New post   12 Feb 2010, 23:50
Do we really need to know till power of 2?? not even 3?
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bangalorian2000
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Re: 5 roots in one equation [#permalink] New post   12 Feb 2010, 23:57
testprep2010 wrote:
(x-a)(x-b)(x-c)(x-d)(x-e)
= x^5
- (a+b+c+d+e) x^4 --[one at a time]
+ (ab+ac+ad+ae+bc+db+be+cd+ce+de...2 at a time) x^3
- (abc+acd+ade+bcd+bce+cde...3 at a time) x^2
+ (abcd+acde+abde+...4 at a time) x
- abcde

x5 − 5x^4 + kx^3 + mx^2 + nx − 1 = 0

How to find sum of products of 2 roots taken at a time ? k

How to find sum of products of 3 roots taken at a time ? -m


Hope this helps!


Good explanation. Kudo given.



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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Re: 5 roots in one equation [#permalink]
12 Feb 2010, 23:57
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