Root
Usage Message:
Root[f, k] represents the kth root
of the polynomial equation f[x] == 0.
Attributes[Root] = {NHoldAll, Protected, ReadProtected}
Options:
ExactRootIsolation
-> False
Notes:
Root is used both for computing and for representing roots of univariate polynomials. Root[f, k] gives the k-th root of the univariate polynomial f. If the result is a root of an irreducible polynomial, then the result is given in the form of another Root expression.
An irreducible polynomial is a polynomial that cannot be factored using integer coefficients. For example, the polynomial x^2 - 2 is irreducible. This polynomial can be factored into x - Sqrt[2] and x + Sqrt[2], but Sqrt[2] is not an integer. Roots of polynomials are called algebraic numbers. In informal usage, the term algebraic number is sometimes used to refer more specifically to roots of irreducible polynomials, or to roots that cannot be represented in terms of radicals. When Root[f, k] appears in a result, the polynomial f is always irreducible. In input f can be any univariate polynomial, and need not be irreducible. In Mathematica Version 3.0, roots of an irreducible polynomial are ordered starting with real roots, followed by complex roots. Real roots are ordered using the natural order of real numbers. If the polynomial is not irreducible, then roots are ordered within factors. This ordering may be changed for some future version of Mathematica.
Additional Online Documentation:
Mathematica 3.0
http://documents.wolfram.com/v3/RefGuide/Root.html
Mathematica 4.0
http://documents.wolfram.com/v4/RefGuide/Root.html
Questions or comments? Send email to support@wolfram.com.
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