Quadratic Equation Solver with Step-by-Step Solutions
Solve any quadratic polynomial equation ax² + bx + c = 0 using the quadratic formula x = (-b ± √(b² - 4ac)) / (2a). Features step-by-step discriminant evaluation, handles complex numbers with imaginary units (i), and calculates parabola vertex and axis of symmetry.
How to Use Quadratic Equation Solver with Steps
Input Coefficients
Enter coefficients a, b, and c (where a ≠ 0).
Evaluate Discriminant
See whether the equation has 2 distinct real roots, 1 repeated real root, or 2 complex roots.
Inspect Parabola Properties
View the vertex (h, k), axis of symmetry x = -b/(2a), and Y-intercept.
About Quadratic Equation Solver with Steps
The discriminant Δ = b² - 4ac reveals the nature of the roots without fully solving the equation: if Δ > 0, there are two distinct real roots (parabola crosses X-axis twice); if Δ = 0, there is one repeated real root (tangent to X-axis); if Δ < 0, roots are complex conjugates (parabola does not touch X-axis).
Key Features
- Standard Quadratic Formula: x = [-b ± √(b² - 4ac)] / (2a)
- Discriminant Analysis: Δ = b² - 4ac (positive, zero, or negative)
- Handles imaginary complex roots in standard a ± bi format
- Calculates Parabola Vertex coordinates and direction of opening
- Detailed step-by-step substitution and radical simplification
Frequently Asked Questions
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