Quadratic Equation Solver
Solve polynomial equations of degree 2: ax² + bx + c = 0
What is a Quadratic Equation Solver?
This tool solves 'Quadratic Equations'—polynomial equations of the second degree, commonly written in the form `ax² + bx + c = 0`. It uses the famous Quadratic Formula to find the roots (values of x) where the parabola crosses the x-axis.
Quadratic equations appear everywhere in physics (projectile motion), engineering (structural design), and economics (profit optimization). Solving them manually involves calculating the 'Discriminant' (`Δ = b² - 4ac`) and then finding the two possible values for x.
Our solver handles all three scenarios automatically: 1) Two distinct real roots (when Δ > 0), 2) One repeated real root (when Δ = 0), and 3) Two complex/imaginary roots (when Δ < 0).
It simplifies the result analysis by clearly stating which type of roots were found and displaying them mathematically. For complex roots, it formats them in the standard `a + bi` notation.
1How to Use
- Identify Coefficients: Look at your equation (e.g., `2x² - 5x + 3 = 0`).
- Enter Values: Input `2` for a, `-5` for b, and `3` for c.
- Solve: Click the 'Solve Equation' button.
- Check Roots: See values for x1 and x2.
- Analyze Type: Read whether the roots are Real, Equal, or Complex (Imaginary).
★Key Features
- Complex Number Support: Correctly handles negative discriminants using `i` notation.
- Discriminant Logic: Automatically detects the nature of the roots.
- Visual Input: Equation format helps you place coefficients correctly.
- Instant Math: No page reloads needed.
- Zero Validation: Prevents division by zero errors (if a=0, it's not quadratic).