The roots of the equation $(x-a)(x-a-1)+(x-a-1)(x-a-2)+(x-a)(x-a-2)=0$,where $a \in R$,are always:

The sum of the non-real roots of $(p^2+p-3)(p^2+p-2)-12=0$ is

If $(x-2)$ is a common factor of the expressions $x^2+ax+b$ and $x^2+cx+d$,then $\frac{b-d}{c-a}$ is equal to

If the roots of the equation $x^2 + a^2 = 8x + 6a$ are real,then

Let $\alpha \neq 1$ be a real root of the equation $x^3-a x^2+a x-1=0$,where $a \neq -1$ is a real number. Then,a root of this equation,among the following,is

Let $p(x) = x^2 + ax + b$ have two distinct real roots,where $a, b$ are real numbers. Define $g(x) = p(x^3)$ for all real numbers $x$. Then,which of the following statements are true?
$I.$ $g$ has exactly two distinct real roots.
$II.$ $g$ can have more than two distinct real roots.
$III.$ There exists a real number $\alpha$ such that $g(x) \geq \alpha$ for all real $x$.