Question:
If $\alpha, \beta$ are the zeros of the polynomial $f(x)=x^{2}+x+1$, then $\frac{1}{\alpha}+\frac{1}{\beta}=$
(a) 1
(b) $-1$
(c) 0
(d) None of these
Solution:
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)