Find the Zeros of a Quadratic Equation Calculator
Introduction & Importance
Finding the zeros of a quadratic equation is a fundamental concept in mathematics. It helps us determine the points where a quadratic function crosses the x-axis, which is crucial in various fields like physics, engineering, and economics.
How to Use This Calculator
- Enter the coefficients A, B, and C of your quadratic equation (Ax² + Bx + C) in the respective input fields.
- Click the “Calculate” button.
- View the results below the calculator, which include the zeros of the equation and a visual representation using a chart.
Formula & Methodology
The zeros of a quadratic equation can be found using the quadratic formula:
x = [-B ± √(B² – 4AC)] / (2A)
Our calculator uses this formula to find the zeros of your equation.
Real-World Examples
Data & Statistics
| Equation | Zero 1 | Zero 2 |
|---|---|---|
| x² – 5x + 6 | 2 | 3 |
| x² + 3x – 10 | -5 | 2 |
Expert Tips
- Always ensure that the coefficient A is not zero, as it would make the equation linear, not quadratic.
- For real and distinct zeros, the discriminant (B² – 4AC) must be greater than zero.
- For real and repeated zeros, the discriminant must be equal to zero.
Interactive FAQ
What is the discriminant in a quadratic equation?
The discriminant is the value inside the square root in the quadratic formula, which determines the nature of the zeros.