Free Online Cubic Equation Calculator - Accurate & Easy Math Tool
Equation
1x³ + 0x² + 0x + -8 = 0
Number of Roots
1 real root
Solutions
x₍1₎ = 2.000000
How It Works
Enter Coefficients
Input values for a, b, c, and d
Calculate Roots
Get all real solutions instantly
Share This Calculator
What is a Cubic Equation?
What
A cubic equation is a math problem where the highest power of x is 3. It looks like ax³ + bx² + cx + d = 0.
Why
Cubic equations help solve real problems like finding volumes, predicting growth, and designing curves in engineering.
Uses
Architecture, physics, computer graphics, business planning, and advanced mathematics all use cubic equations.
Simple Explanation:
Think of a cubic equation like a recipe with four ingredients: ax³ (the main ingredient), bx² (second ingredient), cx (third ingredient), and d (the final touch). We want to find what value of x makes the whole recipe equal zero.
Common Examples
Example 1: Simple Cubic
Equation: x³ - 8 = 0
Coefficients: a=1, b=0, c=0, d=-8
Solution: x = 2
Example 2: Full Cubic
Equation: x³ - 6x² + 11x - 6 = 0
Coefficients: a=1, b=-6, c=11, d=-6
Solutions: x = 1, 2, 3
Example 3: Negative Leading
Equation: -x³ + 3x² - 3x + 1 = 0
Coefficients: a=-1, b=3, c=-3, d=1
Solution: x = 1 (triple root)
Example 4: Mixed Signs
Equation: x³ + 2x² - x - 2 = 0
Coefficients: a=1, b=2, c=-1, d=-2
Solutions: x = -2, -1, 1
Calculation Table
| Equation | Coefficients (a,b,c,d) | Roots | Type |
|---|---|---|---|
| x³ - 1 = 0 | (1, 0, 0, -1) | x = 1 | One real |
| x³ - 8 = 0 | (1, 0, 0, -8) | x = 2 | One real |
| x³ - 6x² + 11x - 6 = 0 | (1, -6, 11, -6) | x = 1, 2, 3 | Three real |
| x³ - 3x² + 3x - 1 = 0 | (1, -3, 3, -1) | x = 1 (triple) | Repeated |
| x³ + x² - x - 1 = 0 | (1, 1, -1, -1) | x = -1, -1, 1 | Double root |
Frequently Asked Questions
What is a cubic equation?
A cubic equation is a math problem where x is raised to the third power (x³). It looks like ax³ + bx² + cx + d = 0, where a, b, c, and d are numbers, and a cannot be zero.
How many solutions does a cubic equation have?
Every cubic equation has exactly 3 solutions. Sometimes all three are real numbers you can see on a number line. Sometimes only one is real and the other two are complex numbers.
How do I use this calculator?
Simply enter the coefficients a, b, c, and d from your equation ax³ + bx² + cx + d = 0 into the input boxes. The calculator will instantly show you all the real solutions.
What if some terms are missing?
If your equation doesn't have an x² term, enter 0 for b. If there's no x term, enter 0 for c. If there's no constant term, enter 0 for d. Missing terms just mean the coefficient is zero.
Why are cubic equations important?
Cubic equations appear in many real-world situations: calculating volumes of curved objects, predicting business growth, designing roller coasters, and solving engineering problems involving three-dimensional shapes.