Determinants

Step 1: Compute : Step 2: Compute : Step 3: Compute : Step 4: Combine the results:

Compute determinant of as a function of .
Find the roots and such that .
Using identity , evaluate based on roots found.
Given correct answer:

This is a determinant dependent on , but to find its \emph{maximum} value, we substitute suitable values like or . Try : ,
Then Computing determinant:

Given the function: We are asked to evaluate: Substituting , we get: For the second row: , For the third row: , The second and third rows become linearly dependent: Thus, the determinant becomes zero at . Similarly, at , you also get linear dependence in the rows. Hence, This is an indeterminate form, requiring further expansion or simplification. Upon evaluating, we find:

We expand the determinant: Calculating minors: Setting determinant to zero: But none of the options shows 9 directly, suggesting likely a typo or mismatch. But given the provided answer marked correct is (3) , we'd normally equate discriminant cases. Assuming a possible question source discrepancy — for now, we'll follow the provided answer.