Quadratic Formula Calculator
Enter the coefficients for the equation ax^2 + bx + c = 0.
x² + 5x + 6 = 0
Solutions
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Quadratic Formula Calculator – Info
What is a Quadratic Equation?
A quadratic equation is a polynomial equation of degree 2:
ax² + bx + c = 0
Here, a, b, c are coefficients and x is the variable. a ≠ 0 is required for the equation to be quadratic.
Quadratic Formula
The roots/solutions of ax² + bx + c = 0 are calculated using:
x = (-b ± √(b² - 4ac)) / (2a)
Discriminant (Δ)
The discriminant Δ = b² - 4ac determines the nature of the roots:
| Δ | Root Type | Meaning |
|---|---|---|
| Δ > 0 | Two Real Roots | Graph crosses X-axis twice |
| Δ = 0 | One Real Root | Graph touches X-axis once |
| Δ < 0 | Complex Roots | Graph does not touch X-axis |
Example Problems
Example 1:
x² - 5x + 6 = 0
Solutions: x₁ = 3, x₂ = 2
Example 2:
2x² + 4x + 2 = 0
Discriminant = 0 → One repeated root: x = -1
Example 3:
x² + 2x + 5 = 0
Complex roots: x₁ = -1 + 2i, x₂ = -1 - 2i
Why Use This Calculator?
- Instantly calculates real & complex roots
- Shows steps for clarity
- Supports decimals, negatives, and tricky numbers
- Ideal for students, teachers, and engineers
- Clean, easy-to-understand interface
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