Symmetric functions of roots involve expressions that depend on sum and product. For roots α, β: Sum (α + β) = -b/a; Product (αβ) = c/a. Common symmetric functions: (1) α² + β² = (α+β)² - 2αβ; (2) α³ + β³ = (α+β)³ - 3αβ(α+β); (3) 1/α + 1/β = (α+β)/(αβ); (4) α² - β² = (α+β)(α-β). Example: For x² - 5x + 6 = 0, roots are 2 and 3. Sum = 5, product = 6. Then α² + β² = 25 - 12 = 13. Or 1/α + 1/β = 5/6. Shortcut: Use symmetric properties instead of solving roots. Exam tip: Recognize patterns in questions asking for sums/products of functions of roots.