Rangdom

Solve ax² + bx + c = 0 — enter the three coefficients below.

Roots, discriminant, and vertex of any quadratic

Enter the three coefficients of ax² + bx + c = 0 and the panel applies the quadratic formula x = (−b ± √D) / 2a, updating live as you type. The discriminant D = b² − 4ac decides the nature of the roots: a positive D gives two distinct real roots, a zero D a single repeated root, and a negative D a complex-conjugate pair shown as p ± qi. The parabola’s vertex (−b / 2a, c − b² / 4a) is reported too, and the roots have their own copy button.

All three fields accept decimals and negatives. Because a = 0 removes the x² term, it is not a quadratic and is flagged rather than solved; a neutral empty state and inline messages naming the offending field keep it from ever rendering NaN or Infinity. Everything is computed in your browser with no network calls. Higher-degree polynomials, factoring or step-by-step working, graph plotting, and solving for arbitrary variables are out of scope.