Quadratic Formula Calculator
What is the Quadratic Formula?
The quadratic formula is a fundamental equation in algebra that provides the solutions to any quadratic equation of the form ax² + bx + c = 0. It’s essential for finding roots in physics, engineering, and economics problems.
Quadratic Formula and Explanation
The standard quadratic formula is:
x = [-b ± √(b² – 4ac)] / (2a)
| Variable | Meaning | Typical Range |
|---|---|---|
| a | Coefficient of x² | Any real number ≠ 0 |
| b | Coefficient of x | Any real number |
| c | Constant term | Any real number |
Practical Examples
Example 1: Real Roots
Equation: 2x² + 5x – 3 = 0
Solutions: x = 0.5 and x = -3
Example 2: Complex Roots
Equation: x² + 2x + 5 = 0
Solutions: x = -1 ± 2i
How to Use This Calculator
- Enter numerical values for coefficients a, b, and c
- Click “Calculate Roots”
- Review roots, discriminant, and nature of solutions
- Use reset button for new calculations
Key Factors in Quadratic Equations
- Discriminant value determines root type
- Leading coefficient (a) affects parabola direction
- Real-world applications in projectile motion
- Graphical interpretation of roots
- Importance in optimization problems
- Connection to polynomial factorization
Quadratic Formula FAQ
What if a = 0?
The equation becomes linear, not quadratic.
Can I use decimal coefficients?
Yes, the calculator accepts any real numbers.
How are complex roots displayed?
Results show in a+bi form with imaginary unit i.