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, including those with complex solutions.

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 roots by considering the discriminant (b² - 4ac) which determines the nature of the roots.

3. Importance of Quadratic Formula

Details: The quadratic formula is essential for solving second-degree polynomial equations that appear in various mathematical, scientific, and engineering applications.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will display both solutions, including complex solutions if needed.

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 complex (non-real) solutions. The calculator will display these in complex number form.

Q3: Can I use fractions or decimals?
A: Yes, the calculator accepts both decimal and fractional inputs (like 0.5 or 1/2).

Q4: What if I get only one solution?
A: When the discriminant is exactly zero, there's exactly one real solution (a repeated root).

Q5: How accurate are the results?
A: Results are accurate to 4 decimal places. For exact symbolic solutions, consider using computer algebra systems.