Let P_n =α^n +β^n, n ∈ N. If P_10=123, P_9=76, P_8=47 and P_1=1, then the quadratic equation having roots 1/(α) and 1/(β) is:

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