existence of nth root

If n is a positive integer and a>0 then the polynomialMathworldPlanetmathPlanetmathPlanetmath xn-a[x] has one sign change so by Descartes’s Rule of Signs has a unique positive real root.

Title existence of nth root
Canonical name ExistenceOfNthRoot1
Date of creation 2013-03-22 16:08:38
Last modified on 2013-03-22 16:08:38
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 10
Author Mathprof (13753)
Entry type Proof
Classification msc 26C10
Classification msc 12D99
Classification msc 26A06
Related topic ExistenceOfRoot
Related topic ExistenceOfSquareRootsOfNonNegativeRealNumbers