Multiple Root


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multiple root

[′məl·tə·pəl ′rüt]
(mathematics)
A polynomial ƒ(x) has c as a multiple root if (x-c) n is a factor for some n > 1. Also known as repeated root.

Multiple Root

 

A multiple root of the polynomial

f(x) = aoxn + a1xn-1 + … + an

is a number c such that f(x) is divided without remainder by the binomial (x—c) raised to the second or higher degree; c is called a root of multiplicity k iff(x) is divided by (x—c)k but not by (x—c)k+l. A root of multiplicity k of the polynomial f(x) is also a root of all the derivatives of the polynomial up to and including the derivative of order (k — 1), that is, of the polynomials f’(x), f”(x), & ,f(k-1)(x). A multiple root of the polynomial f(x) is also called a multiple root of the equation f(x) = 0.

References in periodicals archive ?
In section 2, we discuss the Fixed Point Modified Generalized Newton-Raphson (FPMGNR) Method for multiple roots whereas in section 3, we compare FPMGNR Method for multiple roots with the other methods considered in this paper through some numerical examples.
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They cover topics in real and complex number complexity theory; the real solving of algebraic varieties with intrinsic complexity; the complexity and geometry of numerically solving polynomial systems; multiplicity hunting and approximating multiple roots of polynomial systems; the intrinsic complexity of elimination problems in effective algebraic geometry; and Newton iteration, conditioning, and zero counting.
Sormani, Some variants of Newton's method with third order convergence and multiple roots, J.
The Nights has multiple roots from different cultures and its content, that might not be exclusively Oriental, is an issue for many scholars.
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The idea of a global celebration dedicated to the Earth and to environmental issues sprang from multiple roots.

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