Quadratic Equation Solver
Free Online Calculator with Step-by-Step Solutions
Solve ax² + bx + c = 0
Enter the coefficients a, b, and c to find the roots.
x² +
x +
= 0
Roots (x)
Calculating…
Visual Representation of Parabola
Step-by-Step Solution
What is a Quadratic Equation?
Figure 1: Visualizing the curve of a quadratic function
A quadratic equation is a second-degree polynomial equation in a single variable x. The general form is ax² + bx + c = 0, where a, b, and c are constants, and a is not equal to zero. The name “quadratic” comes from “quadratum,” which is Latin for square, because the highest power of the variable is squared (x²).
Quadratic Formula Explained
Figure 2: Learning the math formula step by step
The universal method for solving any quadratic equation is the quadratic formula:
x = (−b ± √(b² − 4ac)) / (2a)
Here is how it works:
- Identify coefficients: Extract a, b, and c.
- Calculate Discriminant (Δ): Compute b² – 4ac.
- Find Roots: Substitute into the formula to find x.
Real-World Applications
Figure 3: Engineering applications of quadratic curves in bridges
Quadratic equations model various real-world phenomena:
- Projectile Motion: Calculating the path of a thrown ball or rocket.
- Engineering: Determining the shape of bridges and cables.
- Area Optimization: Finding dimensions that maximize area.