CWMO 2006 Problem 2

Find the smallest positive real $k$ satisfying the following condition: for any given four DIFFERENT real numbers $a,b,c,d$ , which are not less than $k$ , there exists a permutation $(p,q,r,s)$ of $(a,b,c,d)$ , such that the equation $(x^{2}+px+q)(x^{2}+rx+s)=0$ has four different real roots.