Roots, discriminant and graph
For ax² + bx + c = 0, Δ = b² − 4ac. Positive discriminant gives two real roots, zero a repeated root, and negative two complex roots. With a = 0 the equation is treated as linear.
Example and limitations
x² − 3x + 2 = 0 has roots 1 and 2. The local approximate plot helps understanding but does not cover the whole domain or replace algebraic verification. Decimal arithmetic has JavaScript precision limits.