Enter coefficients a, b, and c for the equation ax² + bx + c = 0. The calculator finds the discriminant, both roots (real or complex), and the vertex of the parabola.
Δ > 0: two distinct real roots. Δ = 0: one repeated real root (parabola touches x-axis). Δ < 0: no real roots, only complex conjugate roots.
Δ = b² − 4ac | If Δ>0: two real roots x = (−b ± √Δ) / 2a | If Δ=0: one double root x = −b/2a | If Δ<0: two complex conjugate roots
Example: x² − 5x + 6 = 0 → Δ = 25−24 = 1 → x₁ = 3, x₂ = 2
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