Certain Polynomials with Weighted Sums

In this note, we provide some examples of polynomials $z^n-p(z)$, where $p(z)={\limits\sum_{k=o}^{n-1}}a_kz^k$, and ${\limits\sum_{k=o}^{n-1}}a_kz^k=1$, $a_k{\geq}0$ for each k such that p(z) has all its zeros on ${\mid}z{\mid}=c<1$, and $z^n-p(z)$ has all its zeros on two circles ${\mid}z{\mid}=1$ and ${\mid}z{\mid}=d<1$.