1. What is the Discriminant?

The discriminant (D) is a component of the quadratic formula that determines the nature of the roots of a quadratic equation. It is calculated from the coefficients of the quadratic equation in the form ax² + bx + c = 0.

2. How Does the Calculator Work?

The calculator uses the discriminant formula:

Where:

• \( a \) — Coefficient of x²
• \( b \) — 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:

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

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will compute the discriminant instantly.

5. Frequently Asked Questions (FAQ)

Q1: What if a is zero?
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 (non-real) roots.

Q3: How precise is the calculation?
A: The calculator provides results rounded to 4 decimal places for clarity.

Q4: What's the geometric interpretation?
A: The discriminant relates to where the parabola (graph of the quadratic) intersects the x-axis.

Q5: Can I use this for higher-degree equations?
A: No, the discriminant is specific to quadratic equations. Cubic equations have a different discriminant formula.