Roots of polynomials

• If p and q are roots of a polynomial $ax^2 +$$bx +$$c =$$0$, then p + q = -b/a and p x q = c/a.
• If p, q and r are roots of a polynomial $ax^3 +$$bx^2 +$$cx +$$d =$$0$, then $\sum p$ = -b/a, $\sum pq$ = c/a and $\sum pqr$ = -d/a.
• If p, q, r and s are roots of a polynomial $ax^4 +$$bx^3 +$$cx^2 +$$dx +$$e =$$0$, then $\sum p$ = -b/a, $\sum pq$ = c/a, $\sum pqr$ = -d/a and $\sum pqrs$ = e/a.
• 1/p + 1/q +...+ 1/n = $\sum p$ / $\sum pq$ for any number of roots.
• $p^n$ x $q^n$ x...x $N^n$ = $\sum pq...N$ for any number of roots.
• $p^2 +$$q^2 +$$...+$$n^2$ = $(\sum p)^2$ - 2 $\sum pq$ for any number of roots.
• $p^3 +$$q^3$ = $(p + q)^2$ - 3 (p x q)(p + q) only for quadratics.
• $p^3 +$$q^3 +$$r^3$ = $(p + q + r)^3$ - 3 (p + q + r)($\sum pq$) + 3 (p x q x r) only for cubics
• If a polynomial has roots p, q, r and s, the polynomial with roots a p + b, a q + b, a r + b and a s + b is given by f((w - b)/a).