1. What is the Quadratic Formula?

The quadratic formula provides the solutions to quadratic equations of the form ax² + bx + c = 0. It is one of the most important formulas in algebra and is used to find the roots (solutions) of any quadratic equation.

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) which determines the nature of the roots.

3. Importance of Quadratic Equations

Details: Quadratic equations appear in various fields including physics, engineering, economics, and optimization problems. They describe parabolic relationships between variables.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will display real or complex roots depending on the discriminant value.

5. Frequently Asked Questions (FAQ)

Q1: What if I get complex roots?
A: Complex roots occur when the discriminant is negative, meaning the parabola doesn't intersect the x-axis. The solutions are valid in complex number system.

Q2: What if coefficient a is zero?
A: The equation becomes linear (not quadratic). The calculator will show an error message in this case.

Q3: How precise are the results?
A: Results are rounded to 4 decimal places for readability, but calculations use full precision.

Q4: Can I use fractions or decimals?
A: Yes, the calculator accepts both decimal and fractional inputs (entered as decimals).

Q5: What are some practical applications?
A: Used in projectile motion calculations, optimization problems, signal processing, and many physics/engineering applications.