In one of my investigations, I needed to figure out sums of powers of roots of polynomial equations. These are not very hard to figure out. For monic polynomials, the first three sums are:
Sum of roots: -a_{n-1}
Sum of squares: a_{n-1}²-2a_{n-2}
Sum of cubes: -a_{n-1}³+3a_{n-1}a_{n-2}-3a_{n-3}
Would anyone have a reference where all of these formulas can be found? Do you know of any applications that these formulas have?