1. What is a Cubic Equation?

A cubic equation is a polynomial equation of degree three. The general form is ax³ + bx² + cx + d = 0, where a ≠ 0. Cubic equations appear in various areas of mathematics, physics, and engineering.

2. How Does the Calculator Work?

The calculator solves the cubic equation:

Where:

• \( a \) — Coefficient of x³ (must be non-zero)
• \( b \) — Coefficient of x²
• \( c \) — Coefficient of x
• \( d \) — Constant term

Explanation: The calculator uses the discriminant method to determine whether there are one real root or three real roots, and calculates them accordingly.

3. Importance of Cubic Equations

Details: Cubic equations are fundamental in mathematics and have applications in physics (e.g., thermodynamics), engineering (e.g., structural analysis), and economics (e.g., optimization problems).

4. Using the Calculator

Tips: Enter the coefficients a, b, c, and d. The coefficient a must be non-zero. The calculator will display all real roots of the equation.

5. Frequently Asked Questions (FAQ)

Q1: What if the equation has complex roots?
A: This calculator only displays real roots. Complex roots occur when the discriminant is negative, but we show the three real roots in trigonometric form.

Q2: Can I solve quadratic equations with this?
A: Yes, by setting a=0, but it's better to use a dedicated quadratic equation solver for that case.

Q3: What's the maximum number of real roots?
A: A cubic equation can have either one real root or three real roots (counting multiplicities).

Q4: How precise are the results?
A: Results are rounded to 4 decimal places. For exact solutions, symbolic algebra systems may be needed.

Q5: What if I get NaN as a result?
A: This might happen with extreme coefficient values that cause numerical overflow. Try adjusting your coefficients.