Quadratic Equation Solver
The quadratic equation solver is an online calculator that finds the solution(s) of equations in the form ax² + bx + c = 0. This tool is widely used in algebra, physics, engineering, and mathematics education.
Solve ax² + bx + c = 0
What Is a Quadratic Equation?
A quadratic equation is a second-degree polynomial equation written as:
ax² + bx + c = 0
The highest power of the variable is 2, which makes it quadratic.
The Quadratic Formula
To solve any quadratic equation, mathematicians use the quadratic formula:
x = (−b ± √(b² − 4ac)) / (2a)
How the Calculator Works
Step 1: Read values of a, b, and c
Step 2: Calculate the discriminant Δ = b² − 4ac
Step 3: Determine the number of solutions
Step 4: Compute x using the quadratic formula
Types of Solutions
The discriminant decides the nature of the solutions:
- Δ > 0 → Two real solutions
- Δ = 0 → One real solution
- Δ < 0 → No real solutions
Example
Solve: x² − 5x + 6 = 0
a = 1, b = −5, c = 6
Δ = (−5)² − 4(1)(6) = 1
x = (5 ± 1) / 2 → x = 2 or x = 3
Conclusion
The quadratic equation solver is an essential math tool for solving polynomial equations quickly and accurately. It helps students understand algebra while saving time on calculations.