JEE Math Practice Question

Let $\mathrm{P}_{\mathrm{n}}=\alpha^{\mathrm{n}}+\beta^{\mathrm{n}}, \mathrm{n} \in \mathrm{N}$. If $\mathrm{P}_{10}=123, \mathrm{P}_9=76, \mathrm{P}_8=47$ and $\mathrm{P}_1=1$, then the quadratic equation having roots $\frac{1}{\alpha}$ and $\frac{1}{\beta}$ is :

1. A.$x^2+x-1=0$
2. B.$x^2-x+1=0$
3. C.$x^2+x+1=0$
4. D.$x^2-x-1=0$