If $p$ and $q$ are prime numbers satisfying the condition $p^{2}-2q^{2}=1$,then the value of $p^{2}+2q^{2}$ is

If one of the roots of the equation $6x^3-25x^2+2x+8=0$ is an integer and $\alpha > 0$,$\beta < 0$ are the other two roots,then $\frac{4}{\alpha}+\frac{1}{\beta}=$

One of the real roots of the equation $x^3-6x^2+6x-2=0$ is

If $x$ is real,then the interval in which no value of the expression $\frac{2(x^2+2x-11)}{2x-5}$ lies,is

Let $\alpha, \beta, \gamma, \delta$ be the roots of the equation $x^4 + x^2 + 1 = 0$. Then the equation whose roots are $\alpha^2, \beta^2, \gamma^2, \delta^2$ 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 $x$.