Quadratic equation

ax² + bx + c = 0 → discriminant, roots, step-by-step solution

ax² + bx + c = 0

D = b² − 4ac. D > 0 — two roots, D = 0 — one root, D < 0 — no real roots (complex: −b/2a ± i·√|D|/2a). Vieta's check: x₁+x₂ = −b/a, x₁·x₂ = c/a — a quick answer verification.

Solution

x₁3.0000

x₂2.0000

D = b² − 4ac = (-5)² − 4·(1)·(6) = 1

√D = 1.0000

x₁ = (−b + √D)/2a = (5 + 1.0000)/2 = 3.0000

x₂ = (−b − √D)/2a = (5 − 1.0000)/2 = 2.0000

Вієт: x₁+x₂ = 5.0000 = −b/a = 5.0000 ✓