Question 28
Let $a,$ $b,$ $c,$ $d$ be real numbers. Suppose that all the roots of $$
z^4+az^3+bz^2+cz+d=0
$$ are complex numbers lying on a circle in the complex plane centered at $0+0i$ and having radius $1.$ The sum of the reciprocals of the roots is necessarily
z^4+az^3+bz^2+cz+d=0
$$ are complex numbers lying on a circle in the complex plane centered at $0+0i$ and having radius $1.$ The sum of the reciprocals of the roots is necessarily