Question 143
Find the smallest positive real number $k$ such that for any four given distinct real numbers $a$, $b$, $c$ and $d$, each greater than or equal to $k$, there exists a permutation $p$, $q$, $r$ and $s$ of $a$, $b$, $c$ and $d$ such that the equation
$$
(x^2 + px + q)(x^2 + rx + s) = 0
$$
has four distinct real roots.
$$
(x^2 + px + q)(x^2 + rx + s) = 0
$$
has four distinct real roots.