If `alpha and beta` are roots of the equation `x^(2)+5|x|-6=0,` then the value of `|tan^(-1)alpha-tan^(-1)beta|` is

Options

A. `pi/2`
B. `0`
C. `pi`
D. `pi/4`

Answer

A

Explanation

Given `alph` and `beta` be the roots of the equation
`x^(2) + 5|x| - 6= 0`
Now, `|x|^(2) + 5|x| - 6 = 0`
`|x|^(2 ) + 6|x| - |x|- 6 = 0`
[by factorisation]
`|x|(|x| +6) - 1(|x|+6) = 0`
`(|x|+6)(|x|-1) = 0`
`|x| = - 6` or `|x| = 1`
(Since, modulus cannot be giving negative values )
`:. |x| = 1 rArr x = +- 1`
So, `alpha = 1` and `beta = -1`
`:.` Now, `|tan^(-1) alpha - tan^(-1) beta| = |tan^(-1) 1 - tan^(-1)(-1)|`
`= |pi/4 - (-pi/4)| = |(pi)/(4) + (pi)/(4)| = |pi/2|`