84d67c88   
   XPost: sci.math, sci.math.num-analysis   
   From: goddardbe@netscape.net   
      
   pnachtwey  wrote in news:d47c3576-ea88-4d27-   
   be75-18dd8ddf6033@w24g2000prd.googlegroups.com:   
      
   > I need to determine if there is a zero or root between two points   
   for   
   > a polynomial y=f(x).  f(x) is a fourth order polynomial and the   
   > 'forbidden zone'  is between x0 to x1 where x0 is always at 0.  I   
   > don't need to know where the root is. I just need to quickly find   
   if   
   > there is a root in the 'forbidden zone'. What makes this a little   
   > harder is that there will normally be roots at x0 and x1.   I can   
   find   
   > the number of positive roots by counting the sign changes of the   
   > coefficients of the polynomial.  I can offset the time by x1-eps   
   and   
   > find the number of roots again. If the count is different then I   
   know   
   > a root exists between 0 and x1.   
      
   If x0 and x1 are, in fact, roots, you can divide g(x) by   
   x-x0 and x-x1, leaving a quadratic, which is easily solved   
   for the other two roots.   
      
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