If `alpha\ a n d\ beta` are the roots of `4x^2+3x+7=0` then the value of `1/alpha+1/beta` is
a)`4/7` b) `-3/7` c) `3/7` d) `-3/4`

Explanation

To solve the problem, we need to find the value of \( \frac{1}{\alpha} + \frac{1}{\beta} \) given that \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( 4x^2 + 3x + 7 = 0 \).

### Step-by-Step Solution:

1. **Identify the coefficients of the quadratic equation**:
The given quadratic equation is \( 4x^2 + 3x + 7 = 0 \).
Here, the coefficients are:
- \( a = 4 \) (coefficient of \( x^2 \))
- \( b = 3 \) (coefficient of \( x \))
- \( c = 7 \) (constant term)

2. **Use Vieta's formulas to find \( \alpha + \beta \) and \( \alpha \beta \)**:
According to Vieta's formulas:
- The sum of the roots \( \alpha + \beta = -\frac{b}{a} = -\frac{3}{4} \)
- The product of the roots \( \alpha \beta = \frac{c}{a} = \frac{7}{4} \)

3. **Calculate \( \frac{1}{\alpha} + \frac{1}{\beta} \)**:
We can rewrite \( \frac{1}{\alpha} + \frac{1}{\beta} \) as:
\[ \frac{1}{\alpha} + \frac{1}{\beta} = \frac{\alpha + \beta}{\alpha \beta} \]
Substituting the values we found:
\[ \frac{1}{\alpha} + \frac{1}{\beta} = \frac{-\frac{3}{4}}{\frac{7}{4}} \]

4. **Simplify the expression**:
Dividing by a fraction is the same as multiplying by its reciprocal:
\[ \frac{1}{\alpha} + \frac{1}{\beta} = -\frac{3}{4} \times \frac{4}{7} = -\frac{3}{7} \]

5. **Final answer**:
Therefore, the value of \( \frac{1}{\alpha} + \frac{1}{\beta} \) is \( -\frac{3}{7} \).

### Conclusion:
The correct option is **b) -3/7**.