# 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 ?
Lizhi, "A new fourth-order iterative- method for finding multiple roots of nonlinear equations," Applied Mathematics and Computation, vol.
Inspired by the work in this direction, here we present a third order scheme of one-point methods without memory for multiple roots. The proposed scheme involves one evaluation of f, f', and f" each per step.
Let [gamma] be a given polar, not a multiple root of f(z, w) (fixed in what follows), i.e., f([gamma](w), w) [not equal to] 0.
The Generalized Extrapolated Newton-Raphson Method (GEN-R) considered by Vatti VBK et, al  for the multiple root of equation (1.1) is given as
It is to note that the method (1.4) is generally applied for finding a multiple root of equation (1.1) knowing the multiplicity of root in advance.
Values are 75% lower at the 0.5-mm distance relative to a single root system; however, water content gradients are higher for the multiple root system than a single root at the 1.5-mm distance for 2 and 4 h.
g., CAS(1)) may mean that a multiple root is presented in one time.
In this case [a.sub.1] is a multiple root and for the example given is a root of multiplicity three.
PCI Express was not designed to support this environment and so non-transparent bridges are introduced to support a multiple root complex connection.
Hurricane winds and seas batter them--here their multiple root system is a great advantage.
I face a room of 30 seniors who look as though they're about ready to have multiple root canals instead of spending one class period in senior English.

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