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Cubic Equation Solver

Math
Calculators

Solve cubic equations of the form ax³ + bx² + cx + d = 0 easily.

Cubic Equation Solver

ax³ + bx² + cx + d = 0



2x³ - 4x² - 22x + 24 = 0
Enter coefficients to solve the equation.

Provide the values for a, b, c, and d to find the solution.

2. Theory

Transform the equation into the depressed cubic form:

x = y - b/(3a)

Cardano coefficients:

p = (3ac - b²) / (3a²)
q = (2b³ - 9abc + 27a²d) / (27a³)

Finding solutions for a cubic equation can involve complex numbers and requires specific methods to find real roots.

Discriminant:

Δ = q² / 4 + p³ / 27

If Δ > 0: one real root and two complex roots

If Δ = 0: multiple real roots

If Δ < 0: three real roots

Description
Solve cubic equations of the form ax³ + bx² + cx + d = 0 easily. Enter the coefficients a, b, c, and d to find the roots of the equation. This tool provides step-by-step solutions and explanations for better understanding.
Categories
Math
Calculators