Newton's Formula for Power Sums of Zeros | |||
---|---|---|---|
2 | 1 | 2 | -2 |
1 | 2 | 2 | 2 |
-2 | 3 | -6 | 4 |
3 | 4 | 12 | -26 |
58 | |||
-88 | |||
54 | |||
174 | |||
-752 | |||
1702 | |||
-2466 | |||
1204 | |||
5718 | |||
-22678 |
Let be the sum of the nth powers of all of the roots of a polynomial equation
then
where . This can be seen trivially for a 3rd degree polynomial
so