The sum of all the solutions of the equation $(8)^{2x} - 16 \cdot (8)^x + 48 = 0$ is:

The roots of the equation $x^4+x^3-4x^2+x+1=0$ are diminished by $h$ so that the transformed equation does not contain the $x^2$ term. If the values of such $h$ are $\alpha$ and $\beta$,then $12(\alpha-\beta)^2=$

If the sum of two particular roots of the equation $x^4-4x^3-7x^2+22x+24=0$ is equal to the sum of the remaining two roots,then the sum of the cubes of all the roots of this equation is

For what values of $a \in \mathbb{Z}$,the quadratic expression $(x+a)(x+1991)+1$ can be factorised as $(x+b)(x+c)$,where $b, c \in \mathbb{Z}$?

If $m$ and $M$ are respectively the smallest and greatest rational roots of the equation $6x^6-25x^5+31x^4-31x^2+25x-6=0$,then $M-m=$

For the equation $|x^2| + |x| - 6 = 0$,the roots are