1. What is the Quadratic Formula?

The quadratic formula is a fundamental equation in algebra that provides the solution(s) to quadratic equations of the form ax² + bx + c = 0. It's derived from completing the square of the general 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
• \( \pm \) — Indicates two possible solutions

Explanation: The term under the square root (\( b^2 - 4ac \)) is called the discriminant and determines the nature of the roots.

3. Understanding the Solutions

Three cases based on discriminant:

1. Positive discriminant: Two distinct real roots
2. Zero discriminant: Exactly one real root (a repeated root)
3. Negative discriminant: Two complex conjugate roots

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will show all solutions, including complex ones when they exist.

5. Frequently Asked Questions (FAQ)

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

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

Q3: How precise are the solutions?
A: Solutions 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 any real numbers (including fractions in decimal form).

Q5: What's the geometric interpretation?
A: The solutions represent the x-intercepts (roots) of the parabola y = ax² + bx + c.