Isn't this called Newton's Sums instead of Newton sums?
Most people I know call them Newton sums, but I believe the "proper" term is Newton-Gerard Identities. --ComplexZeta 22:41, 22 August 2006 (EDT)
How can the sum of squares equal a negative number (or does the polynomial have imaginary roots?). --Sean 17:22, 7 November 2006 (EST)
Come now, you should be able to figure that one out for yourself (especially since 1 is a root of the polynomial). --JBL 17:31, 7 November 2006 (EST)
OK, wow, stupid question. Whoooops! --Sean 22:35, 7 November 2006 (EST)
Should we change the example to find instead? Reason being, this would show how to use the sums for higher powers, showing that you still only have 4 terms in your equation when you go for a sum that is greater than 4? (i.e. $S_4 + 3S_3 + 4S_2 − 8S_1 = 0$ (Error compiling LaTeX. ! Package inputenc Error: Unicode character − (U+2212)) and then $S_5 + 3S_4 + 4S_3 − 8S_2 = 0$ (Error compiling LaTeX. ! Package inputenc Error: Unicode character − (U+2212)) (Hopefully you get my meaning) (this was something that confused me when I started learning Newton sums). --Sean 22:40, 7 November 2006 (EST)