What are the real roots of the equation $x^2 + 5|x| + 4 = 0$?

If $a, b, c, d$ are real numbers such that $a < b < c < d$,then the roots of the equation $(x-a)(x-c)+2(x-b)(x-d)=0$ are

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 $x$.

If the expression $\left( mx - 1 + \frac{1}{x} \right)$ is always non-negative for $x > 0$,then the minimum value of $m$ must be

The midpoint of the diagonal of a rectangle formed by $x^2+5x-6=0$ and $y^2-8y-20=0$ is

If $x = 2 + \sqrt{3}$,then what is the value of $x^3 - 7x^2 + 13x - 12$?