If $\alpha , \beta$ and $\gamma$ are the roots of ${x^3} + 8 = 0$, then the equation whose roots are ${\alpha ^2},{\beta ^2}$ and  ${\gamma ^2}$ is

If the quadratic equation ${x^2} + \left( {2 - \tan \theta } \right)x - \left( {1 + \tan \theta } \right) = 0$ has $2$ integral roots, then sum of all possible values of $\theta $ in interval $(0, 2\pi )$ is $k\pi $, then $k$ equals 

If ${x^2} + px + 1$ is a factor of the expression $a{x^3} + bx + c$, then

The number of real solutions of the equation $|x{|^2}$-$3|x| + 2 = 0$ are

The number of distinct real roots of the equation $|\mathrm{x}+1||\mathrm{x}+3|-4|\mathrm{x}+2|+5=0$, is ...........