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May 11th, 2013, 06:08 AM  #1 
Senior Member Joined: Aug 2011 Posts: 149 Thanks: 0  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? 
May 11th, 2013, 08:43 AM  #2 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  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.

May 11th, 2013, 09:29 AM  #3 
Senior Member Joined: Aug 2011 Posts: 149 Thanks: 0  Re: Need help with proving
how would I show that?

May 11th, 2013, 09:49 AM  #4 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  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. 
May 11th, 2013, 10:15 AM  #5 
Senior Member Joined: Aug 2011 Posts: 149 Thanks: 0  Re: Need help with proving
Thank you for your response.


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