Algebra: Roots and Coefficients

Concept Explanation

For a quadratic ax² + bx + c = 0 with roots α and β, Vieta's formulas link roots to coefficients without solving fully.

Vieta's Formulas

• α + β = −b/a
• αβ = c/a
• x² − (sum)x + (product) = 0 for monic quadratics

Derived Results

• α² + β² = (α + β)² − 2αβ
• ( α − β )² = (α + β)² − 4αβ

Example

For x² − 5x + 6 = 0: sum = 5, product = 6, roots 2 and 3.

Common Trap

Sign matters: sum = −b/a, not b/a.