1. What is the Quadratic Formula?

The quadratic formula provides the solutions to quadratic equations of the form ax² + bx + c = 0. It's a fundamental tool in algebra that works for all quadratic equations, whether they have real or complex roots.

2. How Does the Calculator Work?

The calculator uses the quadratic formula:

Where:

• \( a \) — Coefficient of x² (must not be zero)
• \( b \) — Coefficient of x
• \( c \) — Constant term

Explanation: The formula calculates the roots by considering the discriminant (b² - 4ac). If discriminant is positive, there are two real roots; if zero, one real root; if negative, two complex roots.

3. Importance of Quadratic Formula

Details: The quadratic formula is essential for solving second-degree equations in mathematics, physics, engineering, and many other fields. It's particularly useful when factoring is difficult or impossible.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will display both roots, whether they are real or complex numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if a = 0?
A: If a = 0, the equation is linear, not quadratic. The calculator requires a non-zero value for a.

Q2: What does a negative discriminant mean?
A: A negative discriminant indicates the equation has complex (non-real) roots. The calculator will display these in terms of i (√-1).

Q3: How accurate are the results?
A: Results are calculated to high precision and rounded to 4 decimal places for display.

Q4: Can this calculator handle very large numbers?
A: Within reasonable limits of PHP's floating-point arithmetic. Extremely large numbers may cause precision issues.

Q5: Why is it called "TI 84" calculator?
A: This calculator mimics the functionality of quadratic formula solvers found on popular graphing calculators like the TI-84 series.