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 information about the roots of the quadratic equation without actually solving it.

3. Importance of Discriminant

Details: The discriminant tells us:

• If D > 0: Two distinct real roots
• If D = 0: Exactly one real root (a repeated root)
• If D < 0: No real roots (two complex conjugate roots)

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. All values must be numbers (can be positive, negative, or zero).

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 calculation?
A: The calculator shows results rounded to 4 decimal places.

Q4: What's the relationship between discriminant and parabola?
A: The discriminant relates to where the parabola intersects the x-axis (roots).

Q5: Can I use this for higher-degree polynomials?
A: No, the discriminant is specific to quadratic equations. Cubic and quartic equations have more complex discriminants.