Sure Polynomial Roots

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#1188

From: Jon
Date: Thu, 05 Aug 2004 06:41

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If r is the root to the nth degree polynomial

a[0]+a[1]t+a[2]t^2+...+a[n]t^n=0

Then r is the solution to,
*******************************************
a[0]*ln|r|=

   n
-SUM(1/p)*a[p]*c^p
  p=1

   n
+SUM(1/p)*a[p]
  p=1

      infinity
-a[0]SUM(-1)^(k+1) * a[0]/(k*c^k)
      k=n+1

where
c={(-1)^n * a[0]/a[n] }^(1/n)
*******************************************

This computes roots to a high degree of accuracy and precision.

For an explanation on how this was derived and examples for its use, see 
my web site at,

http://mypeoplepc.com/members/jon8338/polynomial/

Jon Giffen

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