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x = (−b ± √(b²−4ac)) / 2a. Discriminant Δ = b²−4ac: if Δ > 0, two distinct real roots; Δ = 0, one repeated real root; Δ < 0, two complex conjugate roots. Alternatively use factoring (if factorable) or completing the square. Quadratics model projectile motion, economics (profit/revenue), and optimization problems. The vertex is at x = −b/2a.
Solves ax² + bx + c = 0 for real roots.
Two roots
x₁ = 2
x₂ = 3