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 based on the discriminant (b² - 4ac). Positive discriminant gives two real roots, zero gives one real root, and negative gives complex roots.

3. Importance of Quadratic Equations

Details: Quadratic equations appear throughout mathematics and science, describing parabolic motion, optimization problems, and many natural phenomena.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What if I get complex solutions?
A: Complex solutions indicate the parabola doesn't cross the x-axis. They're valid mathematical solutions represented with 'i' (√-1).

Q2: Why can't coefficient a be zero?
A: If a=0, the equation becomes linear (bx + c = 0), not quadratic. The quadratic formula doesn't apply.

Q3: How accurate are the solutions?
A: Solutions are calculated to 4 decimal places for precision.

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

Q5: How is this related to graphing?
A: The solutions represent x-intercepts of the parabola y = ax² + bx + c. Complex solutions mean no real x-intercepts.