Solve cubic equations of the form ax³ + bx² + cx + d = 0.
Coefficients
1x³ + -6x² + 11x + -6 = 0
Roots
3 Distinct Real
x₁3.0000
x₂1.0000
x₃2.0000
About this calculator
Solving Cubic Equations
A cubic equation is a polynomial equation of degree 3. It always has at least one real root. The solutions can be found using the general cubic formula (Cardano's Formula).
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Pro Tips
If Δ > 0, there are 3 distinct real roots.
If Δ = 0, there are repeated real roots.
If Δ < 0, there is 1 real root and 2 complex conjugate roots.
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Fun Facts
"Gerolamo Cardano published the solution in 1545, but he got it from Niccolò Tartaglia, who made him swear a secret oath not to reveal it."
"The discovery of the cubic formula led to the acceptance of complex numbers."
