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April 21st, 2012, 09:48 PM   #1
ray
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the fundamental theorem

1) could you show me how you prove that x = 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
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Re: the fundamental theorem

1.) Write the equation as:



Use the difference of cubes formula:



So, the real root is and the complex conjugate roots we find with the quadratic formula:



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
ray
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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?
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April 21st, 2012, 11:31 PM   #4
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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
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Re: the fundamental theorem

one more question
what is i ? and sqrt(i)?
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April 22nd, 2012, 01:10 AM   #6
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Re: the fundamental theorem



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April 22nd, 2012, 04:50 AM   #7
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Re: the fundamental theorem

Quote:
Originally Posted by MarkFL
Thanks, can you please specify if you can find the imaginary root without knowing the real one?
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