Hello:   
      
   Well, Ok, when I talk about roots, means roots of polynomials, and immediately   
   Riccati equations comes into my mind.   
      
   From my point of view, there is no algebra but differential equations   
   representing them.   
      
   Your question may be answered by someone using simple elementary algebra, I   
   just wanted to let our readers know, what we are up to against in the future.   
      
   Sincerely   
      
   Dr.Mehran Basti   
      
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