Chapter 4 Quadratic Equations

Notes

Quadratic Equation basics: Equation of form ax² + bx + c = 0 a ≠ 0 Example: x² + 5x + 6 = 0 Types: Complete: ax² + bx + c Incomplete: missing b or c Methods to solve: Factorization Break middle term Easy and fast Completing square Make perfect square Useful when factorization fails Quadratic formula x = (-b ± √(b² - 4ac)) / 2a Works always Discriminant: D = b² - 4ac Nature of roots: D > 0 → Real and different D = 0 → Real and equal D < 0 → No real roots Graph idea: Graph is parabola Opens up if a > 0 Opens down if a < 0 Roots = where graph cuts x-axis Important formulas: Sum of roots = -b/a Product of roots = c/a Common mistakes: Sign error in formula Wrong splitting Forget dividing by 2a Ignoring negative roots