Cubic Equation Solver
Degree-three equations resist simple factoring. Enter the coefficients of ax cubed plus bx squared plus cx plus d, and the solver returns all three roots using the Cardano method, with the trigonometric form when all roots are real.
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How to use
- Enter the coefficients of the cubic ax^3 + bx^2 + cx + d (a must not be zero).
- Roots are found with the Cardano method — if all three are real, the trigonometric form is used.
- An example is already entered: x^3 - 6x^2 + 11x - 6, with roots 1, 2 and 3 — use it to check.
Tips
- If the leading coefficient is zero, the equation is not cubic - the tool will tell you.
- One real root plus two complex roots is a normal result, not an error.
- Plug each root back into the equation to double-check your homework.
- The example (roots 1, 2 and 3) is a good sanity check - use it first.
Note: Vieta check: the sum of all three roots is always -b/a and the product is -d/a. Complex roots always come in conjugate pairs when the coefficients are real.
Frequently Asked Questions (FAQ)
What does the cubic equation solver do?
It finds all the roots of a cubic equation ax^3 + bx^2 + cx + d (a must not be zero).
Which method does it use?
Roots are found with the Cardano method. If all three roots are real, the trigonometric form is used.
Is there an example to test?
Yes. An example is pre-filled: x^3 - 6x^2 + 11x - 6, with roots 1, 2 and 3.
What happens if a is zero?
The tool shows an error, because with a at zero the equation is not cubic.