The product of all real roots of the equation $x^2 - |x| - 6 = 0$ is

If the roots of the given equation $(\cos p-1) x^2+(\cos p) x+\sin p=0$ are real,then

If the roots of the equation $x^2+2ax+b=0$ are real,distinct and differ at most by $2m$,then $b$ lies in the interval

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 quadratic equation with real coefficients whose one root is $7 + 5i$ will be:

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 $x$.