1. What is the Second Root of Quadratic Equation?

The second root of a quadratic equation is one of the two solutions that satisfy the equation ax² + bx + c = 0. It is calculated using the quadratic formula with the negative square root operation.

2. How Does the Calculator Work?

The calculator uses the quadratic formula:

Where:

• \( b \) — Numerical coefficient of x in the quadratic equation
• \( D \) — Discriminant of the quadratic equation (b² - 4ac)
• \( a \) — Numerical coefficient of x² in the quadratic equation

Explanation: This formula calculates one of the two possible roots of a quadratic equation, specifically the root obtained by subtracting the square root of the discriminant.

3. Importance of Quadratic Roots Calculation

Details: Calculating quadratic roots is fundamental in algebra and has applications in physics, engineering, economics, and various scientific fields where quadratic relationships occur.

4. Using the Calculator

Tips: Enter the coefficient b, discriminant D, and coefficient a. The discriminant must be non-negative for real roots. Coefficient a cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: What if the discriminant is negative?
A: A negative discriminant indicates that the quadratic equation has complex (imaginary) roots rather than real roots.

Q2: Why are there two roots for a quadratic equation?
A: A quadratic equation is a second-degree polynomial, which means it can have up to two real solutions where the parabola intersects the x-axis.

Q3: What is the relationship between the two roots?
A: The sum of the roots equals -b/a, and the product of the roots equals c/a (Vieta's formulas).

Q4: When does a quadratic equation have only one root?
A: When the discriminant equals zero, the quadratic equation has one real root (a repeated root).

Q5: Can coefficient a be zero?
A: No, if a = 0, the equation becomes linear, not quadratic, and the quadratic formula doesn't apply.