Solve ax² + bx + c = 0.
Solves ax² + bx + c = 0 using the quadratic formula: x = (−b ± √(b² − 4ac)) / (2a).
Discriminant b² − 4ac reveals the nature of the roots: positive → two real roots, zero → one repeated real root, negative → two complex.
Graphically, the roots are where the parabola y = ax² + bx + c crosses the x-axis — a negative discriminant means the parabola never touches the x-axis at all, which is why the roots become complex rather than real.
1x² − 3x + 2 = 0: x₁ = 2, x₂ = 1.
Roots are complex conjugates. The tool reports them as a ± bi.
Then it's not quadratic — it's linear (bx + c = 0). Solve as x = −c/b.
Because a quadratic can have up to two distinct solutions — the plus and minus versions of the square root term each give one of the two roots.