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...

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...

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...

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

third complete proofs of the fundamental theorem of algebra, made contributions to number theory, and developed the theories of binary and ternary quadratic...

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...

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...

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

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...

function#Liouville's theorem. There is a short proof of the fundamental theorem of algebra based upon Liouville's theorem. A consequence of the theorem is that "genuinely...

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

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...

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...

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...

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

theorem of algebra states that the field of complex numbers is algebraically closed. Another example of an algebraically closed field is the field of...

In algebra, the fundamental theorem of algebraic K-theory describes the effects of changing the ring of K-groups from a ring R to R [ t ] {\displaystyle...

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

algebraic proof is known. The fundamental theorem of algebra is a corollary of Hopf's theorem. Dropping the requirement of commutativity, Hopf generalized...

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each...

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

rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity of M; and...

mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship...

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...

problem of algebra was to solve univariate polynomial equations. This problem was completely solved during the 19th century; see Fundamental theorem of algebra...

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...

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...

of any non‐zero complex number, which follows from the fundamental theorem of algebra. In the algebra of quaternions – where the fundamental theorem does...