Relations between the coefficients of a polynomial and quantities s_k defined by s_k=r₁^k + r₂^k + ... + r_n^k, where r₁, ..., r_n are the roots of the polynomial; for the polynomial a₀xⁿ + a₁x^n-1 + ... + a_n , the relations are a₀s_k + a₁s_k-1 + ... + a_k-1s₁ + ka_k = 0, for k < n and a₀s_k + a₁s_k-1 + ... + a_ns_k-n = 0, for k > n.