1. What Is Function Equations Calculator?

The Function Equations Calculator solves quadratic equations of the form ax² + bx + c = 0. It provides real and complex solutions based on the discriminant value, helping users find roots of quadratic functions efficiently.

2. How Does The Calculator Work?

The calculator uses the quadratic formula:

Where:

• \( a \) — Coefficient of x²
• \( b \) — Coefficient of x
• \( c \) — Constant term

Explanation: The discriminant (b² - 4ac) determines the nature of roots:

• Positive discriminant: Two distinct real roots
• Zero discriminant: One real root (repeated)
• Negative discriminant: Two complex conjugate roots

3. Importance Of Equation Solving

Details: Solving quadratic equations is fundamental in mathematics, physics, engineering, and economics. It helps find critical points, optimize functions, and model various real-world phenomena.

4. Using The Calculator

Tips: Enter coefficients a, b, and c. Coefficient a must be non-zero. The calculator will display real or complex solutions based on the discriminant value.

5. Frequently Asked Questions (FAQ)

Q1: What if coefficient a is zero?
A: If a = 0, the equation becomes linear (bx + c = 0), which this calculator does not handle. Please ensure a ≠ 0.

Q2: How are complex roots displayed?
A: Complex roots are shown in the form a ± bi, where a is the real part and b is the imaginary part.

Q3: What precision does the calculator use?
A: Results are rounded to 4 decimal places for clarity while maintaining reasonable accuracy.

Q4: Can this calculator solve higher-degree equations?
A: No, this calculator is specifically designed for quadratic equations (degree 2).

Q5: Are there any limitations to this calculator?
A: The calculator handles standard quadratic equations but may not work with extremely large or small coefficients due to floating-point precision limitations.