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The given quadratic equation is:

\[
3x^2 - 6x - 12 = 0
\]

We are asked to find the sum of the roots of this equation.

### Sum of Roots of a Quadratic Equation

For any quadratic equation in the standard form:

\[
ax^2 + bx + c = 0
\]

The sum of the roots is given by the formula:

\[
\text{Sum of roots} = -\frac{b}{a}
\]

In the equation \(3x^2 - 6x - 12 = 0\), we can identify the coefficients:
- \(a = 3\)
- \(b = -6\)
- \(c = -12\) (though \(c\) is not needed for the sum of roots)

Using the formula for the sum of the roots:

\[
\text{Sum of roots} = -\frac{-6}{3} = \frac{6}{3} = 2
\]

Thus, the sum of the roots is **2**, which corresponds to option B.

Let me know if you would like further clarification or a more detailed explanation!

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Here are 5 related questions to expand your understanding:
1. What is the product of the roots of the quadratic equation \(3x^2 - 6x - 12 = 0\)?
2. How do you factor a quadratic equation like \(3x^2 - 6x - 12 = 0\)?
3. What is the discriminant of this quadratic equation, and what does it tell you about the nature of the roots?
4. How would you solve \(3x^2 - 6x - 12 = 0\) using the quadratic formula?
5. Can you graph the function \(y = 3x^2 - 6x - 12\) and interpret the roots visually?

**Tip**: For any quadratic equation, the sum of the roots depends only on the coefficients of \(x^2\) and \(x\), and you can calculate it without needing to solve the equation fully.

The sum of the roots of 3x^2 - 6x - 12 = 0 is

Learn how to find the sum of the roots for the quadratic equation 3x^2 - 6x - 12 = 0 using Vieta's formulas. Understand key algebraic concepts and apply the formula -b/a to calculate the solution. Suitable for students in Grades 8-10.

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