From: DBRS28A@prodigy.com (Mr. Gerald A. Sabin)
Newsgroups: sci.math
Subject: Re: Please help me about Bairstow method
Date: 29 Jul 1998 14:16:36 GMT

Bairstow's method for finding roots of a polynomial starts
out by assuming a value for a quadratic factor of the
polymonial.
Then checks to see 'how closely' this quadratic factor
divides into the polynomial.
The 'adjusts the coefficients' of the quadratic factor
and checks again for 'how closely' it divides...

This is done repeatedly until 'how closely' is 
'close enough'.

The quadratic factor that fits now has two of the
roots of the polynomial.
The pair of roots may real, or complex.
Divide the quadratic factor into the polynomial and obtain
a 'reduced polynomial'; the original degree N is now N-2.

Procedure is repeated to look for the next quadratic factor.

Should have mentioned that if the degree of the original
is ODD, then there will be at least one real root.
This one real root is found by successive approximation.

Bairstow's method can be readily prepared as a program in
QBASIC.  After that, you can solve for the roots of polynomials
all day long.
-Jerry 29 July 98 1015AM  -0400
  email: Jerry_Sabin.NOSPAM@prodigy.com
  (remove .NOSPAM)