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Topic: product of the roots (Read 446 times) |
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tony123
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product of the roots
« on: Nov 7th, 2007, 11:58am » |
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prove the product of the roots of
50x^50+ 49x^49+ · · · + x + 1 = 0.
is= 1/50.
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| « Last Edit: Nov 7th, 2007, 11:59am by tony123 » |
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Aryabhatta
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Re: product of the roots
« Reply #1 on: Nov 7th, 2007, 12:01pm » |
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If I understood the question correctly, this is a basic question and I believe should be in easy.
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pex
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Re: product of the roots
« Reply #2 on: Nov 7th, 2007, 12:24pm » |
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on Nov 7th, 2007, 12:01pm, Aryabhatta wrote:| If I understood the question correctly, this is a basic question and I believe should be in easy. |
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I agree. Just to be thorough:
| hidden: | Let the roots be r1, r2, ..., r50. By the Fundamental Theorem of Algebra,
50x50 + 49x49 + ... + x + 1 = 50(x-r1)(x-r2)...(x-r50).
Multiplying out, we see that the constant term is 50r1r2...r50. As the constant term needs to be equal to one, the result follows. |
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Grimbal
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Re: product of the roots
« Reply #3 on: Nov 8th, 2007, 1:28am » |
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And what would be the sum of the roots? 
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