Root
The roots of an equation
 | (1) |
for which the equation is satisfied. The Fundamental Theorem of Algebra states that everyPolynomial equation of degree 
has exactly roots, where some roots may have a multiplicity greater than 1 (inwhich case they are said to be degenerate).To find the th roots of a Complex Number, solve the equation 
. Then
 | (2) |
 | (3) |
 | (4) |
proved that any number has th roots (Boyer 1968, p. 476). Householder (1970) gives an algorithm forconstructing root-finding algorithms with an arbitrary order of convergence. Special root-finding techniques can often beapplied when the function in question is a Polynomial.See also Bailey's Method, Bisection Procedure, Brent's Method, Crout's Method, Descartes' SignRule, False Position Method, Fundamental Theorem of Symmetric Functions, Graeffe's Method,Halley's Irrational Formula, Halley's Method, Halley's Rational Formula, Horner's Method,Householder's Method, Hutton's Method, Isograph, Jenkins-Traub Method,Laguerre's Method, Lambert's Method, Lehmer-Schur Method, Lin's Method, Maehly'sProcedure, Muller's Method, Newton's Method, Polynomial, Ridders' Method, RootDragging Theorem, Schröder's Method, Secant Method, Sturm Function,Sturm Theorem, Tangent Hyperbolas Method, Weierstraß Approximation Theorem
References
Arfken, G. ``Appendix 1: Real Zeros of a Function.'' Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 963-967, 1985. Boyer, C. B. A History of Mathematics. New York: Wiley, 1968. Householder, A. S. The Numerical Treatment of a Single Nonlinear Equation. New York: McGraw-Hill, 1970. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Roots of Polynomials.'' §9.5 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 362-372, 1992.
- Plus or Minus
- Plus Perfect Number
- Plus Sign
- Plutarch Numbers
- Plücker Characteristics
- Plücker Relations
- Plücker's Conoid
- Plücker's Equations
- Pochhammer Symbol
- Pocklington-Lehmer Test
- Pocklington's Criterion
- Pocklington's Theorem
- Poggendorff Illusion
- Pohlke's Theorem
- Poincaré-Birkhoff Fixed Point Theorem
- Poincaré Conjecture
- Poincaré Duality
- Poincaré Formula
- Poincaré-Fuchs-Klein Automorphic Function
- Poincaré Group
- Poincaré-Hopf Index Theorem
- Poincaré Hyperbolic Disk
- Poincaré Manifold
- Poincaré Metric
- Poincaré Separation Theorem