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 for finding roots of quadratic equations.

2. How Does the Calculator Work?

The calculator uses the quadratic formula:

Where:

• \( a \) — Coefficient of x²
• \( b \) — 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 (real or complex).

3. Importance of Quadratic Factorization

Details: Finding roots is essential for solving quadratic equations, graphing parabolas, and analyzing various mathematical and real-world problems involving quadratic relationships.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What if the discriminant is negative?
A: The equation will have complex roots, which the calculator displays with imaginary components.

Q2: What if a = 0?
A: The equation becomes linear, not quadratic. The calculator requires a ≠ 0.

Q3: How accurate are the results?
A: Results are accurate to 4 decimal places, sufficient for most practical purposes.

Q4: Can this be used for factoring?
A: Yes, knowing the roots (r₁, r₂) allows you to write the factored form as a(x - r₁)(x - r₂).

Q5: What's the geometric interpretation?
A: The roots represent the x-intercepts of the parabola described by the quadratic equation.