What equations can this solve?

It solves quadratic equations (degree 2) and cubic equations (degree 3), returning every root including complex ones.

How are the roots computed?

Quadratics use the quadratic formula x = (−b ± √(b² − 4ac)) / 2a. Cubics use Cardano's method, with the trigonometric form when all three roots are real.

Why must the leading coefficient be non-zero?

If a = 0 the equation is no longer the chosen degree. Set a to any non-zero value, or lower the degree to match your equation.

Polynomial Roots Calculator

Find the real and complex roots of quadratic and cubic equations.

Find polynomial roots exactly

Enter the coefficients of a quadratic (ax² + bx + c) or cubic (ax³ + bx² + cx + d) equation and this tool returns all roots, including complex ones shown in a + bi form.

Quadratics use the quadratic formula and its discriminant; cubics use Cardano’s method, switching to the trigonometric solution when all three roots are real. Every calculation runs locally in your browser.