Solving Quadratic Equations Not Equal to Zero Calculator
Introduction & Importance
Solving quadratic equations not equal to zero is a fundamental aspect of algebra. This calculator simplifies the process, making it accessible to everyone.
How to Use This Calculator
- Enter the coefficients A, B, and C of your quadratic equation (Ax² + Bx + C = 0).
- Click ‘Calculate’.
- View the results and chart below.
Formula & Methodology
The quadratic formula is used to solve quadratic equations: x = [-B ± √(B² – 4AC)] / (2A). This calculator uses this formula to find the roots of your equation.
Real-World Examples
Example 1
Equation: 2x² – 7x + 3 = 0
Roots: x = [7 ± √(49 – 24)] / 4 = 2, 1.5
Example 2
Equation: x² – 5x + 6 = 0
Roots: x = [5 ± √(25 – 24)] / 2 = 3, 2
Example 3
Equation: x² + 2x – 3 = 0
Roots: x = [-2 ± √(4 + 12)] / 2 = -1, -3
Data & Statistics
| Equation | Roots |
|---|---|
| 2x² – 7x + 3 = 0 | x = 2, 1.5 |
| x² – 5x + 6 = 0 | x = 3, 2 |
| x² + 2x – 3 = 0 | x = -1, -3 |
Expert Tips
- Always check your answers by substituting them back into the original equation.
- Remember, the discriminant (B² – 4AC) determines the nature of the roots.
Interactive FAQ
What if the discriminant is negative?
If the discriminant is negative, the equation has no real roots. It has two complex roots.
Can I solve cubic or higher degree equations with this calculator?
No, this calculator only solves quadratic equations.