1. What is the Quadratic Discriminant?

The discriminant (D) of a quadratic equation \( ax^2 + bx + c = 0 \) is the part under the square root in the quadratic formula. It determines the nature of the roots of the equation.

2. How Does the Calculator Work?

The calculator uses the discriminant formula:

Where:

• \( a \) — Coefficient of \( x^2 \)
• \( b \) — Coefficient of \( x \)
• \( c \) — Constant term

Explanation: The discriminant reveals the nature of the roots:

• \( D > 0 \): Two distinct real roots
• \( D = 0 \): One real root (a repeated root)
• \( D < 0 \): Two complex conjugate roots

3. Importance of Discriminant Calculation

Details: Calculating the discriminant helps determine the number and type of solutions to a quadratic equation without solving it completely. This is crucial in algebra, physics, engineering, and other fields where quadratic equations appear.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation \( ax^2 + bx + c = 0 \). The calculator will compute the discriminant instantly.

5. Frequently Asked Questions (FAQ)

Q1: What if a = 0?
A: If a = 0, the equation is linear, not quadratic. The discriminant concept doesn't apply.

Q2: Can the discriminant be negative?
A: Yes, a negative discriminant indicates complex roots.

Q3: How precise is the calculator?
A: The calculator handles values with up to 4 decimal places for precise calculations.

Q4: What's the relationship between discriminant and parabola?
A: The discriminant tells you how many times the parabola crosses the x-axis (0, 1, or 2 points).

Q5: Can I use this for higher-degree polynomials?
A: No, this calculator is specifically for quadratic (degree 2) equations only.