I am currently in AP Calculus BC and one more year to go, I have heard about Fundamental Theorem of Algebra several times, and with the resources that is out there today I tried to search and study myself. (Also noticed there are some inconsistencies in the versions of explanation about this theorem). But I still wonder why they don't teach this in High School in the USA? Am I wrong? Or do they teach this in other countries?


closed as off topic by Gerry Myerson, Alex Becker, azarel, Austin Mohr, JavaMan Mar 21 '12 at 0:58

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    $\begingroup$ Off-topic - not a question about Mathematics. $\endgroup$ – Gerry Myerson Mar 21 '12 at 0:38
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    $\begingroup$ I do believe that they teach it in some US schools. Generally speaking, though, it isn't really useful for high schoolers to know, insofar as helping them build up technical skill and standard proficiency. It's more something you'd use for a proof. $\endgroup$ – Elchanan Solomon Mar 21 '12 at 0:39
  • $\begingroup$ We learn complex numbers, polynomials then can they at least give some exposure to students who are mathematically inclined $\endgroup$ – Kirthi Raman Mar 21 '12 at 0:43
  • $\begingroup$ HWinslow- Did you really learned the proof, see my answer for further information $\endgroup$ – Victor Mar 21 '12 at 0:46
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    $\begingroup$ This sounds like more of a complaint than a legitimate question. $\endgroup$ – Elchanan Solomon Mar 21 '12 at 0:54

You may need complex analysis or topology to prove it,so this is for advanced undergraduate(junior, senior) , see http://books.google.com/books?id=g0KHD7EIl4cC&printsec=frontcover&dq=fundamental+theorem+of+algebra&hl=en&sa=X&ei=ASNpT-O1B4eMgwfJn4ydCQ&ved=0CDsQ6AEwAA#v=onepage&q=fundamental%20theorem%20of%20algebra&f=false

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    $\begingroup$ Actually, there's a proof that uses only elementary analysis. See, for example, Volume 1 of Mathematical Analysis by Zorich, p 283-284. $\endgroup$ – ItsNotObvious Mar 21 '12 at 1:32

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