Quadratic Equation Solver
Solve ax² + bx + c = 0 for real or complex roots, with the discriminant shown.
ax² + bx + c = 0
Every calculation runs locally in your browser.
Discriminant (b² − 4ac)
1
Roots
x = 2, 1
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What the discriminant tells you before you even solve
The discriminant, b² − 4ac, determines the shape of the answer before you compute a single root: positive means the parabola crosses the x-axis at two distinct points, zero means it just touches the axis at its vertex (one repeated root), and negative means it never crosses the axis at all — the two roots exist only as a complex-conjugate pair, mirror images across the real axis. This is why the quadratic formula, x = (−b ± √(b²−4ac)) / 2a, always produces exactly two answers: the ± sign accounts for both directions from the parabola's axis of symmetry.
Frequently asked questions
What does the discriminant tell me before solving?
The discriminant (b² − 4ac) tells you the nature of the roots before you even compute them: positive means two distinct real roots, zero means one repeated real root, and negative means two complex (non-real) roots.