Example 1
\(x^2 - 5x + 6 = 0 \rightarrow x_1 = 3, x_2 = 2\)
Quadratic Equation Solver
Solve quadratic equations with real and complex solutions
Results
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Theory & Formula
A quadratic equation is a polynomial equation of degree 2, with the general form ax² + bx + c = 0, where a ≠ 0.
The quadratic formula provides the solution(s) to any quadratic equation. The discriminant (b² - 4ac) determines the nature of the roots:
- Δ > 0: Two distinct real roots
- Δ = 0: One real root (double root)
- Δ < 0: Two complex conjugate roots
\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Worked Examples
Example 2
\(x^2 - 4x + 4 = 0 \rightarrow x = 2\) (double root)
Example 3
\(x^2 + x + 1 = 0 \rightarrow\) Complex solutions