Cubic Equation Calculator

Enter cubic equation coefficients:

x3   x2   x   = 0

How does the Cubic Equation Calculator work?

Solves for cubic equations in the form ax3 + bx2 + cx + d = 0 using the following methods:
1) Solve the long way for all 3 roots and the discriminant Δ
2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.
This calculator has 5 inputs.

What 4 formulas are used for the Cubic Equation Calculator?

  1. Δ = 4b3d - b2c2 + 4ac3 - 18abcd + 27a2d2
  2. x1 = 2j * Cosine(k/3) - b/(3a)
  3. x2 = l(m + n) + p
  4. x3 = l(m - n) + p

For more math formulas, check out our Formula Dossier

What 7 concepts are covered in the Cubic Equation Calculator?

cubic equation
An equation of the form ax3 + bx2 + cx + d = 0
a statement declaring two mathematical expressions are equal
Polynomials with a maximum term degree as the second degree
rational root theorem
used to find the rational solutions of a polynomial equation
synthetic division
a shorthand method for dividing a polynomial by a linear factor
a number or value we do not know

Example calculations for the Cubic Equation Calculator

  1. 2x^3 - 4x^2 - 22x + 24