2 Find the smallest positive real number $k$ such that for any 4 distinct real numbers $a, b, c, d$ not less than $k$, there exists a permutation $p, q, r, s$ of $a, b, c, d$ such that the equation
$$
\left(x^{2}+p x+q\right)\left(x^{2}+r x+s\right)=0
$$

has 4 distinct real roots. (Supplied by Feng Zhigang)
The required minimum positive real number $k=4$.
On one hand, if $k4(d-a)>0, c^{2}-4 b>4(c-b)>0$, so (1) and (2) each have two distinct real roots.

On the other hand, if (1) and (2) have a common real root $\beta$, then $\left\{\begin{array}{l}\beta^{2}+d \beta+a=0, \\ \beta^{2}+c \beta+b=0,\end{array}\right.$ Subtracting the two equations, we get $\beta=\frac{b-a}{d-c}>0$, at this time, $\beta^{2}+d \beta+a>0$, which is a contradiction. Therefore, (1) and (2) do not have a common real root.
Thus, $k=4$ meets the requirement.
In summary, the answer to the problem is $k=4$.