In the quadratic equation `2 x^ 2 + 7 x + 3 = 0` then sum of roots is

Options

A. `-7/2`
B. `7/2`
C. `5/3`
D. `-5/3`

Answer

To find the sum of the roots of the quadratic equation \(2x^2 + 7x + 3 = 0\), we can use the formula for the sum of the roots of a quadratic equation, which is given by:

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

where \(a\) is the coefficient of \(x^2\) and \(b\) is the coefficient of \(x\).

### Step-by-Step Solution:

1. **Identify the coefficients**:
- From the equation \(2x^2 + 7x + 3 = 0\), we identify:
- \(a = 2\) (coefficient of \(x^2\))
- \(b = 7\) (coefficient of \(x\))

2. **Apply the formula for the sum of the roots**:
- Using the formula, we substitute the values of \(a\) and \(b\):
\[ \text{Sum of roots} = -\frac{b}{a} = -\frac{7}{2} \]

3. **Conclusion**:
- Therefore, the sum of the roots of the quadratic equation \(2x^2 + 7x + 3 = 0\) is \(-\frac{7}{2}\).

### Final Answer:
The sum of the roots is \(-\frac{7}{2}\).