Quadratic Equation Calculator
Free Quadratic Equation Calculator: Solve quadratic equations (ax² + bx + c = 0) for real or complex roots and find the discriminant.
Inputs
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Result
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More Information
Understanding the Quadratic Equation Calculator
A quadratic equation is a second-degree polynomial equation in a single variable 'x' of the form ax² + bx + c = 0, where 'a' cannot be zero. This calculator is a powerful tool to solve these equations instantly.
How It's Solved: The Quadratic Formula
The roots (solutions for 'x') are found using the well-known quadratic formula:
x = [-b ± sqrt(b² - 4ac)] / 2a
The Discriminant (b² - 4ac)
The part of the formula under the square root, b² - 4ac, is called the discriminant. It's a critical value because it tells us the nature of the roots without fully solving the equation:
- If the discriminant is **positive**, there are two distinct real roots.
- If the discriminant is **zero**, there is exactly one real root (a "repeated root").
- If the discriminant is **negative**, there are two complex roots (involving imaginary numbers).
Our calculator finds the discriminant and then proceeds to calculate the roots, handling all three cases correctly.