1. Fundamental Theorem Of Algebra - Wikipedia, The Free Encyclopedia In mathematics, the fundamental theorem of algebra states that every non constant single-variable polynomial with complex coefficients has at least one http://en.wikipedia.org/wiki/Fundamental_theorem_of_algebra

Fundamental theorem of algebra From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics , the fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root . Equivalently, the field of complex numbers is algebraically closed Sometimes, this theorem is stated as: every non-zero single-variable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted up to its multiplicity . Although this at first appears to be a stronger statement, it is a direct consequence of the other form of the theorem, through the use of successive polynomial division by linear factors. In spite of its name, there is no purely algebraic proof of the theorem, since any proof must use the completeness of the reals (or some other equivalent formulation of completeness), which is not an algebraic concept. Additionally, it is not fundamental for modern algebra ; its name was given at a time in which algebra was mainly about solving polynomial equations with real or complex coefficients. Contents History Proofs Complex-analytic proofs Topological proofs ... edit History Peter Rothe (Petrus Roth), in his book

2. Fundamental Theorem Of Algebra - Encyclopedia Article - Citizendium Dec 11, 2008 The Fundamental Theorem of Algebra is a mathematical theorem stating that every nonconstant polynomial whose coefficients are complex http://en.citizendium.org/wiki/Fundamental_Theorem_of_Algebra

Fundamental Theorem of Algebra From Citizendium, the Citizens' Compendium Jump to: navigation search addthis_pub = 'citizendium'; addthis_logo = ''; addthis_logo_color = ''; addthis_logo_background = ''; addthis_brand = 'Citizendium'; addthis_options = ''; addthis_offset_top = ''; addthis_offset_left = ''; Main Article Talk Related Articles Bibliography External Links This is a draft article , under development and not meant to be cited; you can help to improve it. These unapproved articles are subject to edit intro The Fundamental Theorem of Algebra is a mathematical theorem stating that every nonconstant polynomial whose coefficients are complex numbers has at least one complex number as a root. In other words, given any polynomial (where is any positive integer), we can find a complex number so that One important case of the Fundamental Theorem of Algebra is that every nonconstant polynomial with real coefficients must have at least one complex root. Since it is not true that every such polynomial has to have at least one real root (as the example demonstrates), many mathematicians feel that the complex numbers form the most natural setting for working with polynomials.

3. Fundamental Theorem Of Algebra - Definition The fundamental theorem of algebra (now considered something of a misnomer by many mathematicians) states that every complex polynomial of degree n has http://www.wordiq.com/definition/Fundamental_theorem_of_algebra

Fundamental theorem of algebra - Definition The fundamental theorem of algebra (now considered something of a misnomer by many mathematicians) states that every complex polynomial of degree n has exactly n zeroes, counted with multiplicity. More formally, if (where the coefficients a a n can be real or complex numbers), then there exist ( not necessarily distinct) complex numbers z z n such that This shows that the field of complex numbers , unlike the field of real numbers , is algebraically closed n a and the sum of all the roots equals - a n The theorem had been conjectured in the 17th century but could not be proved since the complex numbers had not yet been firmly grounded. The first rigorous proof was given by Carl Friedrich Gauss in 1799. (An almost complete proof had been given earlier by d'Alembert .) Gauss produced several different proofs throughout his lifetime. All proofs of the fundamental theorem necessarily involve some analysis , or more precisely, the concept of continuity of real or complex polynomials. The main difficulty in the proof is to show that every non-constant polynomial has at least one zero. We mention approaches via complex analysis topology , and algebra Find a closed disk D of radius r p z p z r p z D is therefore achieved at some point z in the interior of D p z m p z ) is a holomorphic function in the entire complex plane. Applying

4. Fundamental Theorem Of Algebra - Simple English Wikipedia, The Free Encyclopedia The fundamental theorem of algebra is a proven fact that is the basis of mathematical analysis, the study of limits. It was proven by German mathematician http://simple.wikipedia.org/wiki/Fundamental_theorem_of_algebra

Fundamental theorem of algebra From Wikipedia, the free encyclopedia Jump to: navigation search The fundamental theorem of algebra is a proven fact that is the basis of mathematical analysis , the study of limits . It was proven by German mathematician Carl Friedrich Gauss . It says that for any polynomial f x with the degree n , where n f must have at least one root , and not more than n roots alltogether. A root is a number x so that f x Some remarks: the degree n of a polynomial is the highest power of x that occurs in it some of the roots may be complex numbers it is possible to 'count' the root r twice, if r is still a root of the polynomial g x f x x r ; if you will 'count' the roots in this way, then the polynomial f x with degree n has exactly n roots many people say that the theorem's name is wrong because it is used more in analysis than algebra This short article about mathematics or a similar topic can be made longer. You can help Wikipedia by adding to it Retrieved from " http://simple.wikipedia.org/wiki/Fundamental_theorem_of_algebra Category Mathematics Hidden category: Math stubs Personal tools New features Log in / create account Namespaces Page Talk Variants Views Read Change View history Actions Search Getting around Main Page Simple start Simple talk New changes ... Give to Wikipedia Print/export Make a book Download as PDF Page for printing Toolbox What links here Related changes Special pages Permanent link ... Cite this page In other languages Català Česky Dansk Deutsch ... Tiếng Việt This page was last changed on 25 April 2010, at 18:21.

5. CiteULike: Scis0000002's Fundamental_theorem_of_algebra [1 Article] Oct 21, 2010 Recent papers added to Scis0000002 s library classified by the tag fundamental_theorem_of_algebra. You can also see everyone s http://www.citeulike.org/user/Scis0000002/tag/fundamental_theorem_of_algebra

6. Article About "Fundamental Theorem Of Algebra" In The English Wikipedia On 24-Ju The fundamental theorem of algebra (now considered something of a misnomer by many mathematicians) states that every complex polynomial of degree n has exactly n zeroes, counted with http://july.fixedreference.org/en/20040724/wikipedia/Fundamental_theorem_of_alge

The Fundamental theorem of algebra reference article from the English Wikipedia on 24-Jul-2004 (provided by Fixed Reference : snapshots of Wikipedia from wikipedia.org) Fundamental theorem of algebra Time you got around to sponsoring a child The fundamental theorem of algebra (now considered something of a misnomer by many mathematicians) states that every complex polynomial of degree n has exactly n zeroes, counted with multiplicity. More formally, if (where the coefficients a a n can be real or complex numbers), then there exist ( not necessarily distinct) complex numbers z z n such that This shows that the field of complex numbers , unlike the field of real numbers , is algebraically closed n a and the sum of all the roots equals - a n The theorem had been conjectured in the 17th century but could not be proved since the complex numbers had not yet been firmly grounded. The first rigorous proof was given by Carl Friedrich Gauss in 1799. (An almost complete proof had been given earlier by d'Alembert .) Gauss produced several different proofs throughout his lifetime. All proofs of the fundamental theorem necessarily involve some analysis , or more precisely, the concept of continuity of real or complex polynomials. The main difficulty in the proof is to show that every non-constant polynomial has at least one zero. We mention approaches via

7. The Fundamental Theorem Of Algebra File Format PDF/Adobe Acrobat Quick View http://www.plu.edu/~stuartjl/Fundamental_Theorem_of_Algebra.pdf

8. Fundamental Theorem Of Algebra: Facts, Discussion Forum, And Encyclopedia Articl Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from http://www.absoluteastronomy.com/topics/Fundamental_theorem_of_algebra

Home Discussion Topics Dictionary ... Login Fundamental theorem of algebra Fundamental theorem of algebra Topic Home Discussion Discussion Ask a question about ' Fundamental theorem of algebra Start a new discussion about ' Fundamental theorem of algebra Answer questions from other users Full Discussion Forum Encyclopedia In mathematics Mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.... , the fundamental theorem Fundamental theorem The fundamental theorem of a field of mathematics is the theorem considered central to that field. The naming of such a theorem is not necessarily based on how often it is used or the difficulty of its proofs.... of algebra states that every non-constant single-variable polynomial Polynomial In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents... with complex Complex number A complex number is a number consisting of a real and imaginary part. It can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit with the property i

9. Wolfram|Alpha: Fundamental Theorem Of Algebra : Statement, Proof, ... Jun 28, 2010 Complete information and computations for fundamental theorem of algebra basic properties, history, http://www.wolframalpha.com/entities/famous_math_problems/fundamental_theorem_of

document.write(''); Home Examples About FAQS ... Media Resources A Wolfram Web Resource Wolfram Research Wolfram Mathematica Wolfram Demonstrations ... Wolfram Tones Enter something to compute or figure out Calculate fundamental theorem of algebra: statement, proof, status, ... Input interpretation: Statement: Alternate statement: History: More Computed by Wolfram Mathematica Download as: PDF Live Mathematica A Wolfram Research Company Participate Entity Index fundamental theorem of algebra: statement, proof, status, ... Input: fundamental theorem of algebra fundamental theorem of algebra Statement Alternate statement Every polynomial P(z) of degree n has n values z_i (some of them possibly degenerate) for which P(z_i) = History

10. Fundamental Theorem Of Algebra In mathematics, the fundamental theorem of algebra states that every non constant single-variable polynomial with complex coefficients has at least one http://www.worldlingo.com/ma/enwiki/en/Fundamental_theorem_of_algebra

Mul tili ngual Ar chi ve Po wer ed by Wor ldLi ngo Fundamental theorem of algebra Home Multilingual Archive Index Ch oo se your la ngua ge: English Italiano Deutsch Nederlands ... Svenska var addthis_pub="anacolta"; Fundamental theorem of algebra In mathematics , the fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root . Equivalently, the field of complex numbers is algebraically closed Sometimes, this theorem is stated as: every non-zero single-variable polynomial, with complex coefficients, has exactly as many complex roots as its degree, if each root is counted up to its multiplicity . Although this at first appears to be a stronger statement, it is an easy consequence of the other form of the theorem, through the use of successive polynomial division by linear factors. In spite of its name, there is no known purely algebraic proof of the theorem, and many mathematicians believe that such a proof does not exist. Besides, it is not fundamental for modern algebra ; its name was given at a time in which algebra was basically about solving polynomial equations with real or complex coefficients.

11. Must Every Linear Operator Have Eigenvalues? If So, Why? [Archive] - Physics For 17 posts 9 authors - Last post Sep 9http//en.wikipedia.org/wiki/fundamental_theorem_of_algebra Well then the proof by the fundamental theorem of algebra falls short of http://www.physicsforums.com/archive/index.php/t-331452.html

Physics Forums Mathematics PDA View Full Version : Must every linear operator have eigenvalues? If so, why? ygolo Aug19-09, 12:48 AM It seems to me that Schur's Decomposition (http://en.wikipedia.org/wiki/Schur_decomposition) relies on the fact that every linear operator must have at least one eigenvalue...but how do we know this is true? I have yet to find a linear operator without eigenvalues, so I believe every linear operator does have at least one eigenvalue. Still how does one prove it? Ben Niehoff Aug19-09, 03:07 AM On a finite-dimensional vector space V over the complex numbers, it should be obvious that any linear operator must have eigenvalues, although some or all of those eigenvalues might be zero. Since the operator is a map from V to itself (or a subset), one can use the pigeonhole principle to show that at least one vector in V must be parallel to its image. Over the real numbers, some operators do not have eigenvalues (e.g. rotation matrices in R^2), because the eigenvalues happen to be complex. But I don't know if this really counts. On an infinite-dimensional vector space, they may be other subtleties that allow an exception. For example, in quantum mechanics, the momentum operator is linear, but its eigenstates are not normalizable, and hence not technically part of the Hilbert space. That is, the eigenvectors are not actually members of the vector space, and so it might be reasonable to say that the corresponding eigenvalues do not actually exist.

12. Top 100 Theorems In Isabelle Feb 10, 2009 Fundamental Theorem of Algebra. theorem fundamental_theorem_of_algebra ~ constant(poly p) zcomplex. poly p z = 0 http://www.cse.unsw.edu.au/~kleing/top100/

The following is a list of the theorems (from this list ) proved so far in the Isabelle theorem proving enviroment. 1. Square root of 2 is irrational theorem prime p p 2. Fundamental Theorem of Algebra theorem ~constant(poly p z ::complex. poly p z 3. Denumerability of the Rational Numbers theorem f f 4. Pythagorean Theorem theorem 5. Prime Number Theorem http://www.andrew.cmu.edu/user/avigad/ - Research Project and TOCL Paper. 7. Law of Quadratic Reciprocity theorem p p q q p q p q * Legendre q p = -1 ^ nat (( p - 1) div 2 * (( q - 1) div 2)) 10. Euler's generalisation of Fermat's Little Theorem theorem m ; zgcd ( x m x ^ phi m = 1] (mod m 11. The Infinitude of Primes theorem p . prime p 15. Fundamental Theorem of Integral Calculus theorem a b x a x x b f x f' x a b f' f b f a 17. DeMoivre's Theorem theorem DeMoivre: cis a n = cis (real n a theorem rcis r a n = rcis ( r n ) (real n a 19. Lagrange's four-square theorem theorem n a b c d a b c d n 20. All primes (1 mod 4) equal the sum of two squares lemma zprime m x y x y m 22. The Non-Denumerability of the Continuum theorem f f 23. Formula for Pythagorean triples corollary zgcd a b a zOdd a b c p q a p q b p q c p q zgcd p q 25. Schroeder-Bernstein Theorem

13. Category:Fundamental Theorem Of Algebra - Wikimedia Commons Nov 12, 2007 CategoryFundamental theorem of algebra. From Wikimedia Commons, the free media repository. Jump to navigation, search http://commons.wikimedia.org/wiki/Category:Fundamental_theorem_of_algebra

Category:Fundamental theorem of algebra From Wikimedia Commons, the free media repository Jump to: navigation search Media in category "Fundamental theorem of algebra" This category contains only the following file. Tfa.svg 15,426 bytes Retrieved from " http://commons.wikimedia.org/wiki/Category:Fundamental_theorem_of_algebra Categories Polynomials Mathematical theorems Personal tools New features Log in / create account Namespaces Category Discussion Variants Views View Edit View history Actions Search Navigation Main Page Welcome Community portal Village pump Participate Upload file Recent changes Latest files Random file ... Donate Toolbox What links here Related changes Special pages Printable version ... Permanent link This page was last modified on 12 November 2007, at 00:03. Text is available under the Creative Commons Attribution/Share-Alike License ; additional terms may apply. See for details. About Wikimedia Commons

14. Fundamental Theorem Of Algebra fundamental theorem of algebra. The result that any polynomial with real or complex coefficients has a root in the complex plane. Related category • ALGEBRA http://www.daviddarling.info/encyclopedia/F/fundamental_theorem_of_algebra.html

15. Fundamental Theorem Of Algebra - Discussion And Encyclopedia Article. Who Is Fun Fundamental theorem of algebra. Discussion about Fundamental theorem of algebra. Ecyclopedia or dictionary article about Fundamental theorem of algebra. http://www.knowledgerush.com/kr/encyclopedia/Fundamental_theorem_of_algebra/

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Sri Lanka Entertainment and Information Portal Home Sri Lanka Photos Sri Lanka Tube Sri Lanka News ... Food Recipes Members Login User ID Password Register Forgot password? Important Links India Tube Videos Property Sri Lanka Bollywood Cinema Online Bali Hotels ... Sri Lanka Hotels Mycities Network Fundamental theorem of algebra Fundamental theorem of algebra Fundamental theorem of algebra From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics , the fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root . Equivalently, the field of complex numbers is algebraically closed Sometimes, this theorem is stated as: every non-zero single-variable polynomial with complex coefficients has exactly as many complex roots as its degree, if each root is counted up to its multiplicity . Although this at first appears to be a stronger statement, it is a direct consequence of the other form of the theorem, through the use of successive polynomial division by linear factors.

17. Proot Taking Too Loooooong ... | TheDailyReviewer http//nostalgia.wikipedia.org/wiki/fundamental_theorem_of_algebra http// education.ti.com/educationportal/sites/US/productDetail/us_polyro= ot_89.html http://thedailyreviewer.com/hardware/view/proot-taking-too-loooooong-116189155

Sign In or Register Browse tags alphabetically: A B C D ... Z Welcome to The Daily Reviewer The Daily Reviewer selects only the world's top blogs (and RSS feeds). We sift through thousands of blogs daily to present you the world's best writers. The blogs that we include are authoritative on their respective niche topics and are widely read. To be included in The Daily Reviewer is a mark of excellence. Proot Taking Too Loooooong ... Below are the coefficients of an Internal Rate of Return (IRR) problem: ] PROOT The above cashflows result into a (period-based) return of 1.164062 % per period (periods are supposed to be months) = 13.968748 % per year. Both my HP17BI+ and my TI BAII Plus Professional give correct answers in about 2 seconds using their standard (built-in) cash-flow routines.. My HP49G+ (2.09) is still running and trying to solve after 2 minutes What is the problem here? Best regards, Peter A. Gebhardt Share on Facebook Share on Twitter Share on Del.icio.us Share on StumbleUpon ... Share on Newsvine On Wed, 20 Sep 2006 16:14:40 -0500, Peter A. Gebhardt wrote: Below are the coefficients of an Internal Rate of Return (IRR) problem= ] PROOT The above cashflows result into a (period-based) return of 1.164062 %

18. Official Mathematics Thread [Archive] - MLG Forums Fundamental Theorem of Algebra (http//en.wikipedia.org/wiki/ fundamental_theorem_of_algebra) If you don t get it A function f(n) (Read f of n, http://www.mlgpro.com/forum/archive/index.php/t-275899.html

MLG Forums Off-Topic Discussion Off-Topic Discussion PDA View Full Version : Official Mathematics Thread -GoDSpeeD 10-13-2009, 09:06 PM For everything mathematics, find help in this thread. Im a junior in high school and I'm taking Accelerated Pre-Calculus and I feel like I'm one of the the few people in my class that get it so I could only imagine how many of you struggle on your math homework. If this should be moved to thought-provoking, feel free to do so moderators. BE NICE, some really need this help. -GoDSpeeD 10-13-2009, 09:07 PM RESERVED YokoKurAmma 10-13-2009, 09:12 PM I dont have math because automotive is a math credit, the only bad thing is we have a half retarded welding teacher trying to teach us simple addition/subtraction of fractions EVERY morning for about 20 minutes. -GoDSpeeD 10-13-2009, 10:08 PM automotive=math credit, sounds like a pretty easy way to go through high school RobWearsPrada 10-13-2009, 10:30 PM Math forum = not necessary.... WMDistraction 10-13-2009, 10:49 PM Math forum = not necessary.... Math is everything. By using this forum, you are involved in a mathematical algorithm.

19. Fundamental Theorem Of Algebra - Professor Global Translate this page 17 ago. 2010 Fundamental theorem of algebra Obtido em http//professorglobal.cbpf.br/ mediawiki/index.php/fundamental_theorem_of_algebra http://professorglobal.cbpf.br/mediawiki/index.php/Fundamental_theorem_of_algebr

20. [isabelle-dev] Classes instance complex acf using fundamental_theorem_of_algebra by ( intro_classes, blast) This would have not been possible without merging some classes. http://www.mail-archive.com/isabelle-dev@mailbroy.informatik.tu-muenchen.de/msg0

isabelle-dev Thread Date [isabelle-dev] classes Amine Chaieb Wed, 07 Nov 2007 19:33:22 +0100 ==== this is no question and no opening for discussion - just for your interest === Dear all, This afternoon, I defined the following class class acf = field + assumes algebraically_closed: "~ constant (poly p) ==> EX x. poly p x = 0" and the following proof: instance complex :: acf using fundamental_theorem_of_algebra by (intro_classes, blast) This would have not been possible without merging some classes. There is a quantifier elimination procedure implemented for complex numbers, which relies on fact easily portable to acf. There is great future in merging classes, so why not roar ahead? Amine. [isabelle-dev] classes Amine Chaieb [isabelle-dev] classes Alexander Krauss [isabelle-dev] classes Amine Chaieb [isabelle-dev] classes Clemens Ballarin Reply via email to

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