Quadratic Equation Calculator
Verified Calculation Engine
The online Quadratic Equation Calculator helps you calculate instantly and solve problems related to Algebra. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Solve quadratic equations of the form ax² + bx + c = 0
x = (-b ± √(b² - 4ac)) / 2a
Quadratic formula for solving ax² + bx + c = 0
- Coefficient a must be nonzero (true quadratic).
- Root classification follows the discriminant D = b² − 4ac.
Inputs
Results
Worked Examples
Example 1: Two distinct real roots
Solve x² - 5x + 6 = 0
- a: 1
- b: -5
- c: 6
- discriminant: 1
- root1: 3
- root2: 2
- type: distinct
Example 2: One repeated root
Solve x² - 4x + 4 = 0
- a: 1
- b: -4
- c: 4
- discriminant: 0
- root1: 2
- root2: 2
- type: repeated
About this calculator
Overview
This quadratic equation calculator solves ax² + bx + c = 0 for real coefficients using the quadratic formula and reports roots based on the discriminant.
When to use
Use it when a problem reduces to a second-degree polynomial equation in one variable.
Inputs explained
- Coefficients a, b, and c with a ≠ 0.
Formula / method
Discriminant D = b² − 4ac. Roots x = (−b ± √D) / (2a) when D ≥ 0 for real roots; D < 0 indicates complex conjugate roots (as implemented by the solver).
Worked example
Example: x² − 5x + 6 = 0 → a = 1, b = −5, c = 6 → D = 1 → roots x = 2 and x = 3.
Interpreting results
D > 0: two distinct real roots; D = 0: one repeated real root; D < 0: no real roots (complex pair).
Assumptions
- Equation is exactly quadratic (a ≠ 0).
- Coefficients are numeric as entered.
Limitations
- Floating-point rounding can affect roots near D ≈ 0.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
Discriminant D = b² − 4ac. Roots x = (−b ± √D) / (2a) when D ≥ 0 for real roots; D < 0 indicates complex conjugate roots (as implemented by the solver).
Example Calculation
Example: x² − 5x + 6 = 0 → a = 1, b = −5, c = 6 → D = 1 → roots x = 2 and x = 3.
Frequently Asked Questions
What is Quadratic Equation Calculator?
- This quadratic equation calculator solves ax² + bx + c = 0 for real coefficients using the quadratic formula and reports roots based on the discriminant.
How does Quadratic Equation Calculator work?
- Discriminant D = b² − 4ac. Roots x = (−b ± √D) / (2a) when D ≥ 0 for real roots; D < 0 indicates complex conjugate roots (as implemented by the solver).
Why use this Math Numbers calculator?
- Use it when a problem reduces to a second-degree polynomial equation in one variable.