If α, β are the zeros of the polynomial p(x) = 4x2 + 3x + 7,

Solution:

Since $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $p(x)=4 x^{2}+3 x+7$

$\alpha+\beta=\frac{-\text { Coefficient of } x}{\text { Coefficient of } x^{2}}$

$=\frac{-3}{4}$

$\alpha \beta=\frac{\text { Constant term }}{\text { Coefficient of } x^{2}}$

$=\frac{7}{4}$

We have

$=\frac{1}{\alpha}+\frac{1}{\beta}$

$=\frac{\beta+\alpha}{\alpha \beta}$

$=\frac{-3}{\frac{4}{\frac{7}{4}}}$

$=\frac{-3}{4} \times \frac{4}{7}$

$=\frac{-3}{7}$

The value of $\frac{1}{\alpha}+\frac{1}{\beta}$ is $\frac{-3}{7}$.

Hence, the correct choice is (b)