Multiple Root definition of Multiple Root in the Free Online Encyclopedia.

multiple root [′məl·tə·pəl ′rüt]

(mathematics)

A polynomial ƒ(x) hascas a multiple root if (x-c)ⁿis a factor for somen> 1. Also known as repeated root.

Multiple Root

A multiple root of the polynomial

f(x) = a_oxⁿ + a₁x^n-1 + … + a_n

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.

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No references found			The idea of a global celebration dedicated to the Earth and to environmental issues sprang from multiple roots. Earth Day: how did it originate? by International Business Times - US ed. Combining them into a single number shifts attention away from multiple root causes in need of correction and toward an abstract number. Consider the Downside of OEE by Richard J Schonberger / Manufacturing Engineering And it is an easy step to the realization that each of these elements has multiple root causes. An end to unpleasant behaviors by Hone, Tom; Norwitz, Jeffrey H. / Naval War College Review			multiple midstop multiple modulation multiple module access Multiple Myeloma multiple neuritis multiple neurofibroma multiple neurofibromatosis multiple of direct personnel expense multiple openings multiple personality multiple perspective software development multiple piece rate plan multiple platforms multiple point multiple precision arithmetic multiple pregnancy Multiple Pregnancy in Agricultural Animals Multiple Pregnancy in Humans multiple prime contract Multiple Processes multiple programming Multiple Proportions, Law of multiple reflection multiple reflection echoes multiple resonance Multiple Root multiple sampling multiple scattering Multiple Sclerosis multiple series multiple serositis multiple shooting multiple single-level multiple sleep latency test multiple spot welding Multiple Star multiple stratification multiple switchboard multiple target generator multiple tropopause multiple twin quad Multiple Units multiple value Multiple Virtual Storage multiple winding multiple x-y recorder multiple zone multiple zone recording multiple-access computer multiple-access network multiple-access service			Multiple Representation Environment Multiple Requests Terminal Multiple Requirements Operations Center Multiple Reservations per Cycle - Cyclic Session Termination Multiple Reservations per Cycle - Immediate Session Termination Multiple Resistance Deletable Element Multiple Resolution Bitmap Compiler multiple resonance Multiple Resonance Filter Array Multiple Resort Ownership Plan Multiple Resource Host Architecture Multiple Resource Management Area Multiple Respiratory Gas Monitoring Multiple Response Question Multiple Response Surface Multiple retinal hemorrhages Multiple Return Rates multiple risk multiple risk multiple risk multiple risk multiple risk Multiple Risk Factor Intervention Trial Multiple Risk Factor Syndrome Multiple Risk Factors Multiple rocket launcher Multiple Rocket Launching System Multiple Room Viewing Multiple Root Multiple roots of a polynomial Multiple roots of a polynomial Multiple roots of a polynomial multiple round lots Multiple Round Simultaneous Impact Multiple Round, Ascending Bid Multiple Routing Configuration Multiple Sail multiple sampling Multiple Satellite Deployment System Multiple Saturation-Recovery Multiple-Echo Multiple Scan Chain Partitioning Multiple Scattered Wave-Self Consistent Field-X Multiple Scatterer Algorithm Multiple scattering Multiple scattering Multiple scattering Multiple scattering Multiple Scattering Relativistic Correlated Multiple Scattering Theory Multiple schlerosis Multiple schlerosis Multiple schlerosis Multiple Sclerose Vereniging Nederland multiple sclerosis multiple sclerosis multiple sclerosis multiple sclerosis multiple sclerosis multiple sclerosis