Answer:
Option A
Explanation:
Given $\alpha$ and $\beta$ be the roots of the equation
x2 +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)
$\therefore$ $|x|=1\Rightarrow x=\pm1$
So, $\alpha$ =1 and $\beta$ =-1 $\therefore$ Now, |$\tan ^{-1} \alpha - \tan ^{-1} \beta$|=|$\tan ^{-1} 1 - \tan ^{-1} -1|$
= $|\frac{\pi}{4}-\left(-\frac{\pi}{4}\right)|=|\frac{\pi}{4}+\frac{\pi}{4}|=|\frac{\pi}{2}|$
