1. What is the Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x with the form ax² + bx + c = 0, where 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
• \( \sqrt{b^2 - 4ac} \) — Discriminant (determines nature of roots)

Explanation: The discriminant (D = b² - 4ac) determines the nature of the roots:

• D > 0: Two distinct real roots
• D = 0: One real double root
• D < 0: 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 coefficients a, b, and c. The coefficient a must not be zero. The calculator will display real or complex solutions as appropriate.

5. Frequently Asked Questions (FAQ)

Q1: What if I get complex roots?
A: Complex roots indicate the parabola doesn't intersect the x-axis. They're valid mathematical solutions used in many engineering applications.

Q2: Why can't coefficient a be zero?
A: If a=0, the equation becomes linear (bx + c = 0), which has a different solution method.

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

Q4: Can I use fractions or decimals?
A: The calculator accepts both decimal inputs (like 0.5) and whole numbers.

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