1. Fundamental Theorem Of Algebra - Wikipedia, The Free Encyclopedia Retrieved from http//en.wikipedia.org/wiki/fundamental_theorem_of_algebra . Categories Abstract algebra Complex analysis Field theory Mathematical 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 stated as: every non-zero single-variable polynomial, with complex coefficients, has exactly as many complex roots as its degree, if repeated roots are counted up to their multiplicity . In other words, for every complex polynomial p of degree n p z n complex solutions, counting multiplicities . 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. Contents History Proofs Complex-analytic proofs Topological proofs ... edit History Peter Rothe (Petrus Roth), in his book

2. Open Dictionary: Top/Mathematics/Complex_Numbers/Fundamental_Theorem_of_Algebra Competing Definitions. Modify Term Fundamental Theorem of Algebra hits=1 votes=1 rating=5.0 Modify Term Fundamental Theorem of Algebra hits=1 votes=1 http://quasor.lunarpages.com/~w3k0002/pages/Top/Mathematics/Complex_Numbers/Fund

Home Help Login Logout ... Random Open Dictionary Dedicated to the pursuit of knowledge Advanced Top Mathematics Complex Numbers ... Fundamental Theorem of Algebra Competing Definitions Fundamental Theorem of Algebra [hits=1 votes=1 rating=5.0] Fundamental Theorem of Algebra [hits=1 votes=1 rating=5.0] : Fundamental Theorem of Algebra from MathWorld Fundamental Theorem of Algebra [hits=1 votes=1 rating=5.0] : Fund theorem of algebra Questions? Bug report? Send email to the Open Dictionary Administrator The Open Dictionary is a World Wide Web of Knowledge (W3K) project.

3. Fundamental Theorem Of Algebra - Conservapedia Retrieved from http//www.conservapedia.com/fundamental_theorem_of_algebra . Category Mathematics. Views. Article; talk page; Edit; History http://www.conservapedia.com/Fundamental_theorem_of_algebra

Fundamental theorem of algebra From Conservapedia Jump to: navigation search The Fundamental theorem of algebra states that every non- zero single- variable polynomial , (possibly with complex coefficients ), has exactly as many complex roots, or solutions, as its degree (the highest power the variable is raised to), if repeated roots are counted when they occur. edit See Also Algebra Retrieved from " http://www.conservapedia.com/Fundamental_theorem_of_algebra Category Mathematics Views Article talk page Edit History Personal tools Log in / create account master control Main Page Educational Index Debate Topics Recent changes ... Random page Help Help Index Desk Statistics Conservapedia Commandments Supreme Court Course Info and Enrollment Supreme Court Project Lectures Search edit console What links here Related changes Upload file Special pages ... Permanent link This page was last modified 18:11, 24 April 2007. This page has been accessed 127 times. About Conservapedia

4. Fundamental Theorem Of Algebra - Encyclopedia Article - Citizendium Retrieved from http//en.citizendium.org/wiki/fundamental_theorem_of_algebra . Categories CZ Live Mathematics Workgroup http://en.citizendium.org/wiki/Fundamental_Theorem_of_Algebra

We are creating the world's most trusted encyclopedia and knowledge base. The general public and experts collaborate, using their real names. Fundamental Theorem of Algebra From Citizendium, the Citizens' Compendium Jump to: navigation search Main Article Talk Related Articles Bibliography External Links This is a draft article , under development. 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 d is any positive integer), we can find a complex number t 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 p x x demonstrates), many mathematicians feel that the complex numbers form the most natural setting for working with polynomials. In fact, a stronger version of the Fundamental Theorem of Algebra is also true: a

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Science Oxygen Home Science Projects Study Reference Notes ... Fundamental Theorem of Algebra... http://books.w3k.org/html/mdft/Fundamental_Theorem_Algebra.html Merak MML browsing... http://merak.pb.bialystok.pl/mmlquery/fillin.php Historia Matematica Mailing List Archive: Re: [HM] The Fundamental Theorem of Al... http://sunsite.utk.edu/math_archives/.http/hypermail/historia/nov98/0016.ht PACIFIC JOURNAL OF MATHEMATICS ... http://nyjm.albany.edu:8000/PacJ/p/2000/196-1-10.pdf [math/0403460] The Multivariate Fundamental Theorem of Algebra and Algebraic Geo... http://arxiv.org/abs/math.AG/0403460 Fundamental Theorem of Algebra... http://ccrma.stanford.edu/~jos/mdft/Fundamental_Theorem_Algebra.html Historia Matematica Mailing List Archive: Re: [HM] The Fundamental Theorem of Al... http://sunsite.utk.edu/math_archives/.http/hypermail/historia/nov98/0065.ht kathryn rice : carl friedrich gauss... http://www.maths.adelaide.edu.au/people/pscott/history/kathryn/Fundamental% Access Denied... http://mathworld.wolfram.com/FundamentalTheoremofAlgebra.html PlanetMath: fundamental theorem of algebra...

6. Fundamental Theorem Of Algebra - Wikipedia Fundamental theorem of algebra. The fundamental theorem of algebra (now considered something of a misnomer by many mathematicians) states that every complex http://facetroughgemstones.com/wikipedia/fu/Fundamental_theorem_of_algebra.html

Office Supplies Buy Posters A-Z Products Website Advertising ... Fundamental theorem of algebra 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 . An easy consequence is that the product of all the roots equals (-1) 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 the early 19th century. (An almost complete proof had been given earlier by d'Alembert .) Gauss produced several different proofs throughout his lifetime. It is possible to prove the theorem by using only algebraic methods, but nowadays the proof based on complex analysis seems most natural. The difficult step in the proof is to show that every non-constant polynomial has at least one zero. This can be done by employing

7. Fundamental Theorem Of Algebra - Simple English Wikipedia, The Free Encyclopedia You can help Wikipedia by adding to it. Retrieved from http//simple.wikipedia. org/wiki/fundamental_theorem_of_algebra . Category Mathematics http://simple.wikipedia.org/wiki/Fundamental_theorem_of_algebra

Fundamental theorem of algebra From the Simple English Wikipedia, the free encyclopedia that anyone can change 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, or highest power, of n , where n f must have exactly n complex zeroes. A zero is a solution to a function for which the number x gives f x . Some of these zeroes may be the same. All polynomials also have at least one zero that is distinct, which means that there is at least one zero that is different from any other zeroes of that function. Many people say that the theorem's name is wrong because it is used more in analysis than algebra. This short article 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 Views Page Talk Change this page History Personal tools Log in / create account Getting around Main Page Community portal Simple talk New changes ... Give to Wikipedia Search Toolbox What links here Related changes Upload file Special pages ... Cite this page In other languages Catal  Česky Dansk Deutsch ... T¼rk§e This page was last changed on 31 December 2007, at 20:22.

8. Fundamental Theorem Of Algebra - AoPSWiki and the rest is all actually algebra. Retrieved from http//www. artofproblemsolving.com/Wiki/index.php/fundamental_theorem_of_algebra http://www.artofproblemsolving.com/Wiki/index.php/Fundamental_Theorem_of_Algebra

AoPSWiki Want to learn how to tackle those tough AMC/AIME/Olympiad counting and probability problems? Check out Art of Problem Solving's NEW by David Patrick. Page Discussion View source History Personal tools Log in / create account Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link Fundamental Theorem of Algebra From AoPSWiki Introduction The fundamental theorem of algebra states that every nonconstant polynomial with complex coefficients has a complex root . In fact, every known proof of this theorem involves a bit of analysis , since a purely algebraic construction of the complex numbers is very hard to work with. Proof One of the shortest proofs of the fundamental theorem of algebra uses Liouville's Theorem of complex analysis , which says that a bounded entire function is constant . Suppose that were a complex polynomial with no complex roots. Then

9. Fundamental Theorem Of Algebra - Indopedia, The Indological Knowledgebase Retrieved from http//www.indopedia.org/fundamental_theorem_of_algebra.html . This page has been accessed 2051 times. This page was last modified 0255, http://www.indopedia.org/Fundamental_theorem_of_algebra.html

Indopedia Main Page FORUM Help ... Log in The Indology CMS In other languages: Deutsch Categories Abstract algebra Complex analysis ... Wikipedia Article Fundamental theorem of algebra ज्ञानकोश: - The Indological Knowledgebase 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

10. AAS_Congruence AAS_Congruence D AAS Congruence AA_Similarity Function_Operations Function_Operations D Function Operations fundamental_theorem_of_algebra fundamental_theorem_of_algebra D Fundamental Theorem http://www.uni-sw.gwdg.de/~hessman/rdf/math/math.txt

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12. Formalizing 100 Theorems In HOL Light fundamental_theorem_of_algebra !p. ~constant(poly p) ?z. poly p z = Cx( 0). 3. The Denumerability of the Rational Numbers DENUMERABLE_RATIONALS http://www.cs.ru.nl/~freek/100/hol.html

1. The Irrationality of the Square Root of 2 2. Fundamental Theorem of Algebra 3. The Denumerability of the Rational Numbers 4. Pythagorean Theorem PYTHAGORAS 5. Prime Number Theorem PNT 7. Law of Quadratic Reciprocity 8. The Impossibility of Trisecting the Angle and Doubling the Cube 10. Euler's Generalization of Fermat's Little Theorem 11. The Infinitude of Primes 14. Euler's Summation of 1 + (1/2)^2 + (1/3)^2 + .... 15. Fundamental Theorem of Integral Calculus 17. De Moivre's Theorem DEMOIVRE 18. Liouville's Theorem and the Construction of Trancendental Numbers LIOUVILLE 19. Four Squares Theorem 20. All Primes (1 mod 4) Equal the Sum of Two Squares 22. The Non-Denumerability of the Continuum 23. Formula for Pythagorean Triples 25. Schroeder-Bernstein Theorem 26. Leibnitz's Series for Pi 30. The Ballot Problem BALLOT 31. Ramsey's Theorem RAMSEY 34. Divergence of the Harmonic Series 35. Taylor's Theorem MCLAURIN 36. Brouwer Fixed Point Theorem BROUWER 37. The Solution of a Cubic

13. Fundamental Theorem Of Algebra - Wikipedia Retrieved from http//nostalgia.wikipedia.org/wiki/fundamental_theorem_of_algebra . This page was last modified 1649, 9 November 2001. http://nostalgia.wikipedia.org/wiki/Fundamental_Theorem_of_Algebra

Fundamental Theorem of Algebra From Wikipedia HomePage Recent changes View source Page history ... Log in Special pages Double redirects Broken redirects Disambiguation pages Log in Preferences My watchlist Recent changes Upload file File list Gallery of new files User list Statistics Random page Orphaned pages Uncategorized pages Uncategorized categories Uncategorized files Uncategorized templates Unused categories Unused files Wanted pages Wanted categories Most linked to pages Most linked to categories Most linked-to templates Pages with the most categories Most linked to files Pages with the most revisions Pages with the fewest revisions Short pages Long pages New pages Oldest pages Dead-end pages Protected pages Protected titles All pages Prefix index List of blocked IP addresses and usernames User contributions What links here Book sources Categories Export pages Version System messages Logs MIME search Search for duplicate files List redirects Unused templates Random redirect Pages without language links File path Search List of Wikimedia wikis Expand templates CategoryTree Gadgets Parser diff test Cross-namespace links Wikimedia Board of Trustees election Search web links Printable version The Fundamental Theorem of Algebra states that every complex polynomial of degree n has exactly n zeroes, counted with multiplicity. More formally, if

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

ALGEBRA A B C ... CONTACT entire Web this site fundamental theorem of algebra The result that any polynomial with real or complex coefficients has a root in the complex plane. Related category ALGEBRA Also on this site: Encyclopedia of History BACK TO TOP var site="s13space1234"

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Wiki: Fundamental theorem of algebra Contents: 1. History 2. Proofs 2. 1. Complex-analytic proofs 2. 2. Topological proofs ... Wapedia: For Wikipedia on mobile phones

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fundamental theorem of algebra Define fundamental theorem of algebra Translate fundamental theorem of algebra fundamental theorem of algebra in Chinese fundamental theorem of algebra in English fundamental theorem of algebra in French fundamental theorem of algebra in Italian ... Download this dictionary fundamental theorem of algebra Translate: English Chinese (S) Chinese (T) Croatian Dutch French German Hebrew Italian Japanese Korean Portuguese Russian Serbian Spanish Swedish Turkish Additional Use Babylon to translate to various languages

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var skin = "monobook"; var stylepath = "/skins"; var wgArticlePath = "/index.php/$1"; var wgScriptPath = ""; var wgServer = "http://sajun.org"; var wgCanonicalNamespace = ""; var wgNamespaceNumber = 0; var wgPageName = "Fundamental_theorem_of_algebra"; var wgTitle = "Fundamental theorem of algebra"; var wgArticleId = 56363; var wgIsArticle = true; var wgUserName = null; var wgUserLanguage = "en"; var wgContentLanguage = "en"; Fundamental theorem of algebra Sajun.org Jump to: navigation The '''fundamental theorem of algebra''' (now considered something of a misnomer by many mathematicians) states that every complex polynomial , ..., ''a'' can be real or complex numbers), then there exist ( not necessarily distinct) complex numbers ''z'' , ..., ''z'' ''n'' field of complex numbers , unlike the field of real numbers , is algebraically closed ''n'' ''a'' and the sum of all the roots equals -''a'' . 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

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Articles Archives Start page News Contact Community General Newsletter Contact information Site map Most recommended Search the site Archive Photo Archive Video Archive Articles Archive More ... Wisdom Archive Body Mind and Soul Faith and Belief God and Religion ... Yoga Positions Site map 2 Site map fundamental theorem of algebra A Wisdom Archive on fundamental theorem of algebra fundamental theorem of algebra A selection of articles related to fundamental theorem of algebra More material related to Fundamental Theorem Of Algebra can be found here: Index of Articles related to Fundamental Theorem Of Al... Fundamental theorem of algebra Page 2 Page 3 ARTICLES RELATED TO fundamental theorem of algebra fundamental theorem of algebra: Encyclopedia II - Quadratic equation - Quadratic formula The quadratic formula explicitly gives the solutions of a quadratic equation in terms of the coefficients , and , which we temporarily assume to be real (but see below for generalizations) with a being non-zero. These solutions are also called the roots of the equation. The formula reads An alternative form sometimes encountered is given by This gives the solutions and . The term is called the discriminant of the quadratic equation, because it discriminat ... See also: Quadratic equation Quadratic equation - Quadratic formula Quadratic equation - Derivation Quadratic equation - Generalizations ... Quadratic equation - History Read more here: fundamental theorem of algebra: Encyclopedia II - Quadratic equation - Quadratic formula The quadratic formula explicitly gives the solutions of a quadratic equation in terms of the coefficients , and , which we temporarily assume to be real (but see below for generalizations) with a being non-zero. These solutions are also called the roots of the equation. The formula reads An alternative form sometimes encountered is given by This gives the solutions and . The term is called the discriminant of the quadratic equation, because it discriminat ...

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