Cubic Equation Solver
Find the real roots of ax^3 + bx^2 + cx + d = 0.
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Request a ToolHow to Use the Cubic Equation Solver
This tool finds all real roots of a cubic polynomial equation.
- Enter coefficients. Provide a (must be non-zero), b, c, and d.
- View the roots. The solver displays one or three real roots depending on the discriminant.
- Copy or share. Use the buttons to copy the result or generate a shareable link.
About Cubic Equations
A cubic equation has the form ax^3 + bx^2 + cx + d = 0 where a is non-zero. Every cubic has at least one real root and at most three. The solver uses Cardano's method: it first reduces the cubic to depressed form, then evaluates the discriminant to determine whether there is one real root (and two complex conjugates) or three distinct real roots. This approach handles all cases including repeated roots.
Frequently Asked Questions
How many roots does a cubic equation have?
A cubic equation always has three roots (counting multiplicity). At least one is real. The other two are either both real or a complex conjugate pair.
What method does this solver use?
It uses Cardano's method, which converts the cubic to depressed form and applies the cubic formula to find the roots.
Why must the leading coefficient (a) be non-zero?
If a is zero, the equation is not cubic. It becomes a quadratic (or lower degree) equation, which requires a different solver.