Given a polynomial a_nxⁿ+a_n–1x^n–1+  ⋅⋅⋅  +a₀ =  0, let s_k denote the sum of the kth powers of the polynomial’s roots. Then Newton’s identities state for k ≥1 that

These identities recursively determine s_k in terms of s_k–1,….,s₁. In these identities a_r is understood to be 0 if r<0. See also elementary symmetric polynomials.