1. What is the Quadratic Equation?

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are coefficients and a ≠ 0. The solutions to this equation are called roots or zeros of the quadratic function.

2. How Does the Calculator Work?

The calculator uses the quadratic formula:

Where:

• \( a \) — Coefficient of x² (cannot be zero)
• \( b \) — Coefficient of x
• \( c \) — Constant term
• \( b^2 - 4ac \) — Discriminant (determines the nature of roots)

Explanation: The discriminant determines the nature of the roots:

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

3. Importance of Quadratic Equations

Details: Quadratic equations appear in various fields including physics, engineering, economics, and computer graphics. They describe parabolic motion, optimize profit functions, and model many natural phenomena.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will solve for x and show both real and complex solutions when applicable.

5. Frequently Asked Questions (FAQ)

Q1: What if coefficient a is zero?
A: If a = 0, the equation becomes linear (bx + c = 0), not quadratic. The calculator requires a ≠ 0.

Q2: How are complex roots represented?
A: Complex roots are shown in the form "a ± bi" where i is the imaginary unit (√-1).

Q3: Can the calculator handle decimal coefficients?
A: Yes, the calculator accepts decimal values for all coefficients.

Q4: What's the significance of the discriminant?
A: The discriminant indicates the nature of the roots without calculating them fully, and determines whether the parabola intersects the x-axis.

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