Polynomial

In mathematics, polynomial functions, or polynomials, are an important class of simple and smooth functions. Here, simple means they are constructed using only multiplication and addition. Smooth means they are infinitely differentiable, i.e., they have derivatives of all finite orders.

Roots

A root or zero of a polynomial f is a number ζ so that f(ζ) = 0. The fundamental theorem of algebra states that a polynomial of degree n over the complex numbers has exactly n complex roots (not necessarily distinct ones). Therefore a polynomial can be factorized as

Related Topics:
'''root''' - Fundamental theorem of algebra

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:f(x) = a_n(x-zeta_1)cdots(x-zeta_{n})

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where each zeta_i is a root of the polynomial f.

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The Abel-Ruffini theorem in algebra states that generally there is no closed formula to calculate the roots of a polynomial of degree 5 or higher. Closed formula means a formula constructed using only the coefficients of the polynomial and the operations of addition, multiplication and exponentiation (and their inverse operations).

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