Quadratic equations ax² + bx + c = 0 have degree 2. Solving methods: (1) Factorization: Express as (px + q)(rx + s) = 0, roots are -q/p and -s/r; (2) Quadratic formula: x = (-b ± √(b² - 4ac))/(2a); (3) Completing square: Rewrite as (x + p)² = q. Discriminant Δ = b² - 4ac determines nature of roots: If Δ > 0, two distinct real roots; If Δ = 0, one repeated root; If Δ < 0, no real roots. Example: x² - 5x + 6 = 0 → (x-2)(x-3) = 0 → x = 2 or 3. Shortcut: Use factorization for integers, formula for decimals. Exam tip: Always check discriminant first. Verify roots by substitution.