Vieta's Formulas

Vieta’s formulas are relationships between the coefficients of a polynomial and the sums and products of its roots (solutions). For a quadratic equation \(ax^2 + bx + c = 0\), the sum of roots equals \(-b/a\), and the product of roots equals \(c/a\). For higher-degree polynomials, these formulas generalize, linking the sums and products of roots to the coefficients in a systematic way. They provide a powerful way to analyze roots without solving the polynomial explicitly, revealing how the shape of the polynomial's solutions is directly connected to its coefficients.