Real roots of polynomials

*To*: mathgroup at smc.vnet.net*Subject*: [mg24688] Real roots of polynomials*From*: Jack Goldberg <jackgold at math.lsa.umich.edu>*Date*: Fri, 4 Aug 2000 01:19:10 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Hi, Suppose Pn[x] is a polynomial of degree n in x. Its coefficients are real. Question: What is a good way of determining the real roots of Pn and their multiplicities? Use NSolve and "cast out" the complex roots and Chop any roots with a "too" small imaginary part (in case NSolve inserts spurious imaginary parts). In cases where n is large and the number of real roots is small compared to n, one can imagine that better methods exist. I have searched MathSource with no real (pun intended) progress. Possibly this is more a math question than a Mathematica question. Help is appreciated. Jack