A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a ≠ 0.
Quadratic equations have at most two solutions (roots), found using the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The discriminant (b² - 4ac) determines the nature of roots: positive → two real roots, zero → one real root, negative → two complex roots. Quadratics model projectile motion, area optimization, and many natural phenomena.
Quadratic equations were solved geometrically by Babylonian mathematicians (2000 BCE). The quadratic formula in its modern form was developed by Brahmagupta (628 CE), then extended by al-Khwarizmi (820 CE).