Sum and product of roots for quadratic ax² + bx + c = 0: Sum of roots (α + β) = -b/a; Product of roots (α × β) = c/a. This avoids solving for individual roots. Constructing equation: If roots are α and β, equation is x² - (α+β)x + αβ = 0. Example: If roots are 3 and -2, sum = 1, product = -6, equation is x² - x - 6 = 0. Applications: (1) Finding symmetric functions of roots; (2) Determining root relationships without calculating roots; (3) Verifying solutions. Shortcut: Check sum/product against given roots immediately. Exam tip: Use this relationship to solve 'find sum of squares of roots': α² + β² = (α+β)² - 2αβ. Practice: Similar problems with different symmetric expressions.