<< I have never seen this done in a textbook. But Bob Churchhouse in his Numerical Analysis course at Cardiff always used to discuss the behaviour of the coefficients as functions of the roots. I thought it a most useful exercise, and did not hesitate to appropriate it for my own course when the time came. WFL
Isn't this relationship -- for a monic polynomial P(x) = (x-r_1)...(x-r_n) = x^n + c_(n-1) x^(n-1) + ... + c_0 just given by the elementary symmetric functions: c_(n-k) = (-1)^k S_k(r_1,...,r_n) where S_k is the sum of all products of the r_j for k distinct indices j ??? But also I wonder how much light this would shed on numerical problems of calculating the reverse relationship: finding the roots from the coefficients. --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx