Quadratic Formula Solver

The quadratic formula is a mathematical formula providing solutions to any quadratic equation ax² + bx + c = 0. The Formula: x = [-b ± √(b² - 4ac)] / 2a Components: • a, b, c: Coefficients from ax² + bx + c = 0 • b² - 4ac: Discriminant (Δ) • ±: Two solutions (using + and −) • 2a: Common denominator The Discriminant (Δ = b² - 4ac): Determines nature of roots: 1. Δ > 0: Two distinct real roots x₁ = [-b + √Δ] / 2a x₂ = [-b - √Δ] / 2a 2. Δ = 0: One repeated real root x = -b / 2a 3. Δ < 0: Two complex conjugate roots x = (-b ± i√|Δ|) / 2a Step-by-Step Process: 1. Identify coefficients a, b, c 2. Calculate discriminant: b² - 4ac 3. Determine nature of roots 4. Substitute into formula 5. Simplify Derivation: From completing the square method Applications: Any quadratic problem, projectile motion, optimization, and parabolic models.