The sum of the roots of the quadratic equation `2x^(2) + 14x + 24 = 0` is ………

Answer

To find the sum of the roots of the quadratic equation \(2x^2 + 14x + 24 = 0\), we can use the formula for the sum of the roots of a quadratic equation, which is given by:

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

### Step-by-Step Solution:

1. **Identify the coefficients**:
The given quadratic equation is \(2x^2 + 14x + 24 = 0\). Here, we can identify the coefficients:
- \(a = 2\) (the coefficient of \(x^2\))
- \(b = 14\) (the coefficient of \(x\))
- \(c = 24\) (the constant term)

2. **Apply the formula**:
Now, we will substitute the values of \(a\) and \(b\) into the formula for the sum of the roots:
\[ \text{Sum of roots} = -\frac{b}{a} = -\frac{14}{2} \]

3. **Calculate the sum**:
Now, we perform the division:
\[ -\frac{14}{2} = -7 \]

4. **Conclusion**:
Therefore, the sum of the roots of the quadratic equation \(2x^2 + 14x + 24 = 0\) is \(-7\).

### Final Answer:
The sum of the roots is \(-7\).

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