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May 11th, 2013, 06:08 AM   #1
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Need help with proving

Hello.

Could anyone help me to prove that:
Prove that when zero points of polynomial are real then .
Hint: vieta's formula.

Here's vieta's formule i've written. Now how do I show that a= b= c = d = 0?


Edit: I found that if x1..x6 were 0 then it works. fut it that formal enough?
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May 11th, 2013, 08:43 AM   #2
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Re: Need help with proving

Not quite. If you can show that the only real solution is then you would have proven that . You have shown that is a solution, but you have not shown that it is the only solution.
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May 11th, 2013, 09:29 AM   #3
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Re: Need help with proving

how would I show that?
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May 11th, 2013, 09:49 AM   #4
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Re: Need help with proving

Here is one way:



Hence,







If all of the x's are real, then their squares must be nonnegative, and hence the only way for the sum of their squares to be equal to 0 is for all of them to be equal to 0.
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May 11th, 2013, 10:15 AM   #5
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Re: Need help with proving

Thank you for your response.
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