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April 21st, 2012, 09:48 PM | #1 |
Member Joined: Nov 2011 Posts: 45 Thanks: 0 | the fundamental theorem
1) could you show me how you prove that x³ = 8 has three roots? is it (x-0) * (x+0) .... 2) Was this theorem invented after the Complex numbers, or it has a justification of its own? 3) What is the practical, concrete use of the other roots, apart from x=2 ? thanks. |
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April 21st, 2012, 10:04 PM | #2 |
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs | Re: the fundamental theorem
1.) Write the equation as: Use the difference of cubes formula: So, the real root is 2.) I believe complex numbers were conceived of before the FTOA. 3.) To give one example, without the complex roots many theorems in classical physics governing harmonic motion would be incomplete. |
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April 21st, 2012, 11:25 PM | #3 |
Member Joined: Nov 2011 Posts: 45 Thanks: 0 | Re: the fundamental theorem
Thanks, Mark. That is how you find the roots. My question is how you prove that a monotonously increasing function has 3 roots? Could you give me a link re point 3? How can the root af any odd power create a problem in physics? Thanks |
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April 21st, 2012, 11:31 PM | #4 |
Member Joined: Nov 2011 Posts: 45 Thanks: 0 | Re: the fundamental theorem
Oh. I forgot, If I got it right you cannot find the complex roots without finding the real root? is that so? Thanks |
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April 22nd, 2012, 01:00 AM | #5 |
Member Joined: Nov 2011 Posts: 45 Thanks: 0 | Re: the fundamental theorem
one more question what is i³ ? and sqrt(i)? |
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April 22nd, 2012, 01:10 AM | #6 |
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs | Re: the fundamental theorem |
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April 22nd, 2012, 04:50 AM | #7 | |
Member Joined: Nov 2011 Posts: 45 Thanks: 0 | Re: the fundamental theorem Quote:
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