1. What is the Difference of Roots of Quadratic Equation?

The Difference of Roots of Quadratic Equation represents the absolute difference between the two roots (x₁ and x₂) of a quadratic equation. It provides insight into the spacing between the roots on the number line.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( D \) — Discriminant of the quadratic equation
• \( a \) — Numerical coefficient of x² term
• \( \sqrt{} \) — Square root function

Explanation: The formula calculates the absolute difference between the two roots of a quadratic equation using the discriminant and the leading coefficient.

3. Importance of Difference of Roots Calculation

Details: Calculating the difference between roots helps in understanding the nature and distribution of solutions to quadratic equations, which is fundamental in algebra and various applied mathematics fields.

4. Using the Calculator

Tips: Enter the discriminant value (must be non-negative) and the numerical coefficient 'a' (cannot be zero). The calculator will compute the difference between the roots.

5. Frequently Asked Questions (FAQ)

Q1: Why must the discriminant be non-negative?
A: The square root of a negative number is not a real number, and this formula calculates the difference between real roots.

Q2: What happens if coefficient 'a' is zero?
A: If a = 0, the equation is not quadratic but linear, and this formula doesn't apply.

Q3: How is this different from the sum of roots?
A: The sum of roots is -b/a, while the difference of roots is √D/a, where D is the discriminant.

Q4: Can this formula be used for complex roots?
A: No, this formula gives the difference between real roots. For complex roots, the concept of "difference" is not defined in the same way.

Q5: What does a large difference value indicate?
A: A large difference indicates that the roots are widely spaced on the real number line.