# fundamental theorem of algebra

fundamental theorem of algebra
Theorem of equations proved by Carl Friedrich Gauss in 1799.

It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers.

* * *

Theorem of equations proved by Carl Friedrich Gauss (Gauss, Carl Friedrich) in 1799. It states that every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers.

* * *

Universalium. 2010.

### Look at other dictionaries:

• 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,… …   Wikipedia

• fundamental theorem of algebra — a theorem in algebra: every equation which can be put in the form with zero on one side of the equal sign and a polynomial of degree greater than or equal to one with real or complex coefficients on the other has at least one root which is a real …   Useful english dictionary

• Fundamental theorem — In mathematics, there are a number of fundamental theorems for different fields. The names are mostly traditional; so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory. Theorems may be… …   Wikipedia

• Fundamental theorem of arithmetic — In number theory, the fundamental theorem of arithmetic (or unique prime factorization theorem) states that every natural number greater than 1 can be written as a unique product of prime numbers. For instance, : 6936 = 2^3 imes 3 imes 17^2 , ,! …   Wikipedia

• Fundamental theorem of linear algebra — In mathematics, the fundamental theorem of linear algebra makes several statements regarding vector spaces. These may be stated concretely in terms of the rank r of an m times; n matrix A and its LDU factorization::PA=LDUwherein P is a… …   Wikipedia

• Fundamental theorem on homomorphisms — In abstract algebra, the fundamental theorem on homomorphisms, also known as the fundamental homomorphism theorem, relates the structure of two objects between which a homomorphism is given, and of the kernel and image of the homomorphism.The… …   Wikipedia

• Fundamental theorem of cyclic groups — In abstract algebra, the fundamental theorem of cyclic groups states that if G, is a cyclic group of order n, then every subgroup of G, is cyclic. Moreover, the order of any subgroup of G, is a divisor of n, and for each positive divisor k, of n …   Wikipedia

• Fundamental — may refer to: * Fundamental frequency,a concept in music or phonetics, often referred to as simply a fundamental . * Fundamentalism, the belief in, and usually the strict adherence to, the simplistic or fundamental ideas based on faith of a… …   Wikipedia

• algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… …   Universalium

• theorem — theorematic /thee euhr euh mat ik, thear euh /, adj. theorematically, adv. /thee euhr euhm, thear euhm/, n. 1. Math. a theoretical proposition, statement, or formula embodying something to be proved from other propositions or formulas. 2. a rule… …   Universalium