
To determine the number of geometrical isomers for the given structure:
Identifying Stereocenters: The given structure contains three stereocenters, which influence the overall geometric configurations.
Counting Geometrical Isomers: The maximum potential geometric isomers can be calculated using the formula:
Total Geometrical Isomers = 2n
where n is the number of stereocenters. In this case:
23 = 8
However, due to symmetry in the molecule, some configurations are equivalent, reducing the number of unique geometrical isomers.
Final Count: Considering the symmetry and equivalent configurations, the total number of unique geometrical isomers for the given structure is 4.
Draw the possible isomers of:
\[ [ \text{Co}(\text{en})_2\text{Cl}_2 ]^+ \]


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: