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