The fundamental theorem of algebra, also called d'Alembert's theorem or the d'Alembert–Gauss theorem, states that every non-constant single-variable polynomial...

in-and-of itself. Fundamental theorem of algebra Fundamental theorem of algebraic K-theory Fundamental theorem of arithmetic Fundamental theorem of Boolean...

exponential of a polynomial. It is named for Jacques Hadamard. The theorem may be viewed as an extension of the fundamental theorem of algebra, which asserts...

vector (i.e. a fixed point of T) spans an invariant subspace of dimension 1. As a consequence of the fundamental theorem of algebra, every linear operator...

infinite) product involving its zeroes. The theorem may be viewed as an extension of the fundamental theorem of algebra, which asserts that every polynomial...

conjugate a − bi is also a root of P. It follows from this (and the fundamental theorem of algebra) that, if the degree of a real polynomial is odd, it must...

produces an output of 0. A root of a polynomial is a zero of the corresponding polynomial function. The fundamental theorem of algebra shows that any non-zero...

complete proofs of the fundamental theorem of algebra. In number theory, he made numerous contributions, such as the composition law, the law of quadratic reciprocity...

short proof of the fundamental theorem of algebra using Liouville's theorem. Proof (Fundamental theorem of algebra) Suppose for the sake of contradiction...

applies Cauchy's residue theorem. Rouché's theorem can also be used to give a short proof of the fundamental theorem of algebra. Let p ( z ) = a 0 + a 1...

influential textbook Algebra. Argand died of an unknown cause on August 13, 1822, in Paris. In 1978 his proof of the fundamental theorem of algebra was called by...

algebraically closed if the fundamental theorem of algebra holds for it. For example, the field of real numbers is not algebraically closed because the polynomial...

that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real...

and the fundamental theorem of algebra. Let D be the division algebra in question. Let n be the dimension of D. We identify the real multiples of 1 with...

many of the older problems of algebra. For example, the proof of the fundamental theorem of algebra demonstrated the existence of complex solutions of polynomials...

Any of a number of fundamental theorems identified in mathematics, such as: Fundamental theorem of algebra, a theorem regarding the factorization of polynomials...

but completely proved only at the beginning of the 19th century. This is the fundamental theorem of algebra, which does not provide any tool for computing...

of notable theorems. Lists of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures List of...

In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational...

century, algebra consisted essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations...

polynomial Fundamental theorem of algebra Hurwitz polynomial Polynomial transformation Tschirnhaus transformation Galois theory Discriminant of a polynomial...

is a version of the fundamental theorem of algebra. In this case, the factorization can be done with root-finding algorithms. The case of polynomials with...

numbers. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics. The best known...

abstract algebra, the fundamental theorem on homomorphisms, also known as the fundamental homomorphism theorem, or the first isomorphism theorem, relates...

bounds of the interval. Applied to the interval of all the real numbers, it gives the total number of real roots of p. Whereas the fundamental theorem of algebra...

In algebraic geometry, Bézout's theorem is a statement concerning the number of common zeros of n polynomials in n indeterminates. In its original form...

The Eilenberg–Niven theorem is a theorem that generalizes the fundamental theorem of algebra to quaternionic polynomials, that is, polynomials with quaternion...

equation, and the fundamental theorem of algebra is named after d'Alembert in French. Born in Paris, d'Alembert was the natural son of the writer Claudine...

representation theorem for Boolean algebras states that every Boolean algebra is isomorphic to a certain field of sets. The theorem is fundamental to the deeper...

integral theorem Computational geometry Fundamental theorem of algebra Lambda calculus Invariance of domain Minkowski inequality Nash embedding theorem Open...