If α, β are the zeros of the polynomial f

Since $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $f(x)=x^{2}+x+1$

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

$=\frac{-1}{1}=1$

$\alpha \times \beta=\frac{\text { constant term }}{\text { coefficient of } x^{2}}$

$=\frac{1}{1}=1$

We have

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

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

$=\frac{-1}{1}$

$=-1$

The value of $\frac{1}{\alpha}+\frac{1}{\beta}$ is $_{-1}$

Hence, the correct choice is (b)