My question is concerning Theorem 3.2 in this paper of Marden's. The gist of the theorem is stated below.
Theorem 3.2.
Every polynomial of the form
$$ f(z) = \sum_{j=0}^{n} (b_j - b_{j-1}) e^{i \theta_j} z^j $$
where
$$ b_{-1} = b_n = 0 < b_0 < b_1 < \cdots < b_{n-1} $$
has all of its zeros in the disk $|z| \leq 1$. Furthermore, every polynomial of the form
$$ g(z) = b_0 + b_1 z + \cdots + b_{n-1} z^{n-1} $$
has all of its zeros in the disk $|z| \leq 1$.
From the way the theorem is worded, it seems like the second part (about the zeros of $g(z)$) follows from the first part. Is this the case?
The theorem is not proved in the paper.
