Let |M| denote the determinant of a square matrix M . Let `g: [ 0 , (pi)/(2)] to RR` be the function defined by `g (theta) = sqrt(f (theta) - 1) + sqrt(f ((pi)/(2) - theta) - 1)`
where

Let p (x) be a quadratic polynomial whose roots are the maximum and minimum values of the function g `(theta)` and p (2) = ` 2 - sqrt2` . then , which of the following is/are TRUE ?

Options

A. `p ((3 + sqrt2)/(4)) lt 0`
B. `p ((1 + 3 sqrt2)/(4)) gt 0`
C. `p ((5 sqrt2 -1)/(4)) gt 0`
D. `p ((5 - sqrt2)/(4)) lt 0`