Quadratic Calculator
Solve quadratic equations using the quadratic formula with step-by-step solutions, discriminant analysis, and detailed explanations. Perfect for algebra and mathematics.
Quadratic Equation Solver
Enter coefficients for ax² + bx + c = 0
Common Quadratic Equations
Click on these links to see instant solutions with common quadratic equations:
Quadratic Equations
A quadratic equation is a polynomial equation of degree 2, written in the standard form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
Quadratic Formula
Where:
• a, b, c are coefficients
• a ≠ 0 (otherwise it's not quadratic)
• Discriminant = b² - 4ac
Discriminant Analysis
| Discriminant (Δ) | Condition | Nature of Roots | Number of Solutions |
|---|---|---|---|
| Δ > 0 | b² - 4ac > 0 | Two distinct real roots | 2 |
| Δ = 0 | b² - 4ac = 0 | One repeated real root | 1 |
| Δ < 0 | b² - 4ac < 0 | Two complex conjugate roots | 2 (complex) |
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Frequently Asked Questions
What is a quadratic equation?
A quadratic equation is a polynomial equation of degree 2, written in the standard form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
What is the quadratic formula?
The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). It provides the solutions to any quadratic equation ax² + bx + c = 0.
What is the discriminant?
The discriminant is b² - 4ac. It determines the nature of the roots: positive discriminant means two real roots, zero means one repeated root, and negative means two complex roots.