Consider the following reactions $ A + HCl + H_2SO_4 \rightarrow CrO_2Cl_2$ + Side Products Little amount $ CrO_2Cl_2(vapour) + NaOH \rightarrow B + NaCl + H_2O $ $ B + H^+ \rightarrow C + H_2O $ The number of terminal 'O' present in the compound 'C' is ______
\( Cr_2O_7^{2-} + HCl + H_2SO_4 \rightarrow CrO_2Cl_2 \)
\( CrO_2Cl_2(vapour) + NaOH \rightarrow Na_2CrO_4 + NaCl + H_2O \)
\( Na_2CrO_4 + H^+ \rightarrow Na_2Cr_2O_7 + H_2O \)
\( 2Na_2CrO_4 + 2H^+ \rightarrow Na_2Cr_2O_7 + 2Na^+ + H_2O \)
\( CrO_4^{2-} \xrightarrow{H^+} Cr_2O_7^{2-} \)
No of terminal "O" = 6
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: