Question 6
Let $a,b$ be the roots of $x^2-px+q=0$ and let $c,d$ be the roots of $x^2-rx+s=0$, where $p,q,r,s$ are positive real numbers. Suppose that
$$M=\frac{2(abc+bcd+cda+dab)}{p^2+q^2+r^2+s^2}$$
is an integer. Determine $a,b,c,d$.
$$M=\frac{2(abc+bcd+cda+dab)}{p^2+q^2+r^2+s^2}$$
is an integer. Determine $a,b,c,d$.