Short result:
Quadratic Equation Solver
Result
Date publish: 16.09.2024
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Author: Calcwizard
Understanding Quadratic Equations
A quadratic equation is a second-degree polynomial equation in the form of ax² + bx + c = 0, where a, b, and c are constants, and a ≠ 0. The solutions to these equations can be found using various methods, including factoring, completing the square, or applying the quadratic formula: x = (-b ± √(b² – 4ac)) / (2a).
Interesting Facts
- The term ‘quadratic’ comes from the Latin word ‘quadratus’, meaning ‘square’.
- Quadratic equations can have two real solutions, one real solution, or two complex solutions depending on the value of the discriminant (b² – 4ac).
- Quadratic equations are widely used in various fields, including physics, engineering, and finance.
Examples of Quadratic Equations
| Equation | Solutions |
|---|---|
| x² – 5x + 6 = 0 | x = 2, x = 3 |
| x² + 4x + 4 = 0 | x = -2 (double root) |
| x² – 2x + 5 = 0 | x = 1 ± 2i (complex solutions) |
| 2x² – 8x + 6 = 0 | x = 1, x = 3 |
Using the Quadratic Equation Solver
To use the Quadratic Equation Solver, simply input the values of a, b, and c from your equation. The calculator will provide the solutions based on the quadratic formula. For instance, if you input a = 1, b = -5, and c = 6, the calculator will show that the solutions are x = 2 and x = 3.
