Quadratic Formula

Definition

The closed-form solution for any quadratic equation ax² + bx + c = 0, where a ≠ 0: x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant b² − 4ac determines the nature of the roots: positive yields two real solutions, zero gives one repeated root, negative produces two complex conjugate roots. Babylonian mathematicians solved quadratic equations as early as 2000 BCE using geometric methods; the modern algebraic form appeared in 9th-century Persian mathematician Al-Khwarizmi's work.