Quadratic Equation Solver
Developed by Hemant Parashar, B.Sc.Solve quadratic equations of the form ax² + bx + c = 0. Supports real and complex roots, discriminant analysis, and vertex coordinates.
General Purpose Disclaimer
This tool is developed for educational and quick reference purposes. Calculations should be verified independently for critical applications.
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Understanding the Quadratic Formula
A quadratic equation is a second-order polynomial equation in a single variable. The general form is:
The solutions (roots) of this equation are calculated using the **quadratic formula**:
Role of the Discriminant (Δ)
The value inside the square root, **D = b² - 4ac**, is called the **discriminant**. It determines the nature of the roots:
- **D > 0:** Two distinct real roots.
- **D = 0:** One real root (a repeated/double root).
- **D < 0:** Two distinct complex conjugate roots (involving the imaginary unit **i**).
The Vertex of a Parabola
The graph of a quadratic equation represents a parabola. The turning point of the parabola is called the **vertex**.
- The x-coordinate of the vertex is: **h = -b / (2a)**.
- The y-coordinate of the vertex is: **k = c - b² / (4a)**.
This tool was developed and verified by Hemant Parashar, B.Sc. Graduate, to provide educational math resources.