Quadratic equations: ax² + bx + c = 0 where a ≠ 0. Roots formula: x = [-b ± √(b² - 4ac)] / 2a. Discriminant (Δ = b² - 4ac) determines root nature: Δ > 0 (two real roots), Δ = 0 (one repeated root), Δ < 0 (no real roots). Shortcut: factorization method for simple cases like (x-p)(x-q) = 0. Vieta's formulas: sum of roots = -b/a, product = c/a. Common traps: sign errors in formula, forgetting ± symbol. Exam tips: check discriminant first, use factorization when possible. Time-saving: recognize perfect square trinomials. Applications: projectile motion, area optimization, profit calculations. Always verify roots using Vieta's relations. Practice discriminant interpretation. Master all three solving methods: factorization, completing square, formula.