Theorem (Vieta's Formulas).   Consider a polynomial of    of degree  n  with roots     

        ,  
        
        .  
        
Let    be the   elementary symmetric function or symmetric polynomial for the variables ,    

          
          
          
          
        ...  
          
          
then
        .  

Moreover, we have the important identities relating the coefficients of    

            for   . 

Exploration

Now we can proceed to explore Vieta's Formulas  for  polynomials of    of degree  .

(c) John H. Mathews 2005