Polynomial Roots Calculator (Cubic)

This calculator finds the real roots of a cubic equation, the values of x that make a third-degree polynomial equal zero. A cubic has the form a x cubed plus b x squared plus c x plus d, and unlike a quadratic, which everyone learns to solve with a neat formula, a cubic is much harder to crack by hand. It always has at least one real root, and may have up to three, and finding them analytically means using Cardano's method, a centuries-old procedure involving cube roots and careful handling of the discriminant. This tool does all of that for you. You enter the four coefficients, a, b, c and d, and the calculator solves the equation, returning the real roots it finds. Cubics appear throughout mathematics, physics and engineering: in modelling curves and volumes, solving equilibrium and motion problems, and anywhere a relationship is genuinely cubic rather than linear or quadratic. Being able to find the roots quickly is invaluable for checking work and solving real problems. The results update as you type, so you can explore how changing a coefficient moves the roots, and see the moment a cubic shifts from having one real root to three. Use it for algebra and calculus homework, for engineering and physics problems, or to factor a cubic once you know its roots. The calculator reports the real roots; a cubic can also have a pair of complex roots, which occur when it crosses the x-axis only once. If you set the leading coefficient to zero, it solves the resulting quadratic or linear equation instead. Results are rounded for display.

Solves ax³ + bx² + cx + d = 0 using Cardano's method. Reports real roots; complex roots occur when the cubic crosses the x-axis once. Rounded for display.