If `alpha, beta (alpha lt beta)` are the roots of the equation `6x^(2) + 11x + 3 = 0`, then which of the following are real ?

Options

A. `cos^(-1) alpha`
B. `sin^(-1) beta`
C. `cosec^(-1) alpha`
D. Both `cot^(-1) alpha and cot^(-1) beta`

Answer

B, C, D

Explanation

`6x^(2) + 11x + 3 = 0`
or `(2x + 3) (3x + 1) = 0`
or `x = -3//2, -1//3`
For `x = -3//2, cos^(-1) x` is not defined as domain of `cos^(-1) x` is `9-1, 1] and " for " x = -1//3, cosec^(-1) x` is not defined as domain of `cosec^(-1)x " is " R -(-1, 1)`. However, `cot^(-1) x` is defined for both of these values as domain of `cot^(-1) x " is " R`