Vieta's formulas

For a monic polynomial xⁿ + aₙ₋₁ xⁿ⁻¹ + ⋯ + a₀ with roots r₁, …, rₙ: the sum of roots is −aₙ₋₁, the product is (−1)ⁿ · a₀, and every elementary symmetric function of the roots is the corresponding coefficient (with alternating signs). Read off without solving.