1. What is the Quadratic Equation?

The quadratic equation is a second-order polynomial equation in a single variable x with the form ax² + bx + c = 0, where a, b, and c are coefficients and a ≠ 0. It has wide applications in physics, engineering, and economics.

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 discriminant (b² - 4ac) determines the nature of the roots:

• Positive discriminant: Two distinct real roots
• Zero discriminant: One real double root
• Negative discriminant: Two complex conjugate roots

3. Importance of Quadratic Equations

Details: Quadratic equations appear in many real-world applications including projectile motion, area calculations, optimization problems, and electrical circuit analysis.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will provide real or complex solutions as appropriate.

5. Frequently Asked Questions (FAQ)

Q1: What if a is zero?
A: If a = 0, the equation becomes linear (bx + c = 0) and has only one solution: x = -c/b.

Q2: Can the calculator handle complex roots?
A: Yes, the calculator will display complex roots in the form a ± bi when the discriminant is negative.

Q3: How precise are the results?
A: Results are rounded to 4 decimal places for clarity.

Q4: What's the geometric interpretation?
A: The roots represent the x-intercepts of the parabola y = ax² + bx + c.

Q5: Are there other methods to solve quadratics?
A: Yes, methods include factoring, completing the square, and graphing, but the quadratic formula works for all cases.