Cubic Equation Calculator

Your details

The leading coefficient. If a = 0 the equation is not cubic and is solved as a quadratic or linear equation instead.
The coefficient of the x-squared term. Enter 0 if this term is absent.
The coefficient of the x term. Enter 0 if this term is absent.
The constant. Enter 0 for a depressed cubic with no constant term.
When the discriminant is positive the two non-real roots are a complex-conjugate pair. Toggle to display them in a + bi form.
How many decimal places to use when displaying roots.
Root(s)Three real roots
x1 = 1, x2 = 2, x3 = 3
Discriminant (Delta)4
Root typeThree distinct real roots (Delta > 0)
Real roots3
x1 (smallest real root)1
Sum of roots (x1 + x2 + x3)6
Product of roots (x1 * x2 * x3)6
Sum of root pairs (x1x2 + x1x3 + x2x3)11

Three distinct real roots found.

  • Every cubic with real coefficients has at least one real root, because its graph runs from -infinity to +infinity and must cross the x-axis somewhere.
  • The discriminant is 4 (positive), confirming three distinct real roots. The graph has a local maximum above the x-axis and a local minimum below it.
  • By Vieta formulas, the three roots must sum to 6 and multiply to 6.

Next stepUse the steps panel above to trace through Cardano formula and the depressed cubic with your exact coefficients.

 = Powered by OnlyCalculators