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...

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

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...

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...

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...

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

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

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...

Exterior algebra F-algebra F-coalgebra Finite field Fundamental theorem of finitely generated abelian groups Gaussian elimination Geometric algebra Gröbner...

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

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...

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

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...

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...

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

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...

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

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...

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...

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

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...

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

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

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...

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...

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...

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