Quadratic Equation Not Equal to Zero Calculator
Introduction & Importance
Quadratic equations not equal to zero are a fundamental concept in algebra, with wide-ranging applications in physics, engineering, and computer science. This calculator helps you solve such equations effortlessly.
How to Use This Calculator
- Enter the coefficients A, B, and C of your quadratic equation.
- Click the “Calculate” button.
- View the results and chart below.
Formula & Methodology
The quadratic formula is used to solve quadratic equations not equal to zero: x = [-b ± √(b² – 4ac)] / (2a)
Real-World Examples
Example 1: Projectile Motion
In physics, the height of a projectile can be modeled by the quadratic equation: h(t) = -16t² + v₀t + h₀, where t is time, v₀ is initial velocity, and h₀ is initial height.
Data & Statistics
| Equation | Discriminant (b² – 4ac) | Number of Real Roots |
|---|---|---|
| x² – 5x + 6 = 0 | 1 | 2 |
| x² + 2x – 3 = 0 | 20 | 2 |
Expert Tips
- Always check the discriminant to determine the nature of the roots.
- For real-life applications, consider the physical meaning of the roots.
Interactive FAQ
What is the discriminant in a quadratic equation?
The discriminant (b² – 4ac) determines the nature of the roots of a quadratic equation.
For more information, see Maths is Fun and Khan Academy.