  We study the root distribution of a sequence of polynomials
$\{P_n(z)\}_{n=0}^{\infty}$ with the rational generating function $$
\sum_{n=0}^{\infty} P_n(z)t^n= \frac{1}{1+ B(z)t^\ell +A(z)t^k}$$ for
$(k,\ell)=(3,2)$ and $(4,3)$ where $A(z)$ and $B(z)$ are arbitrary polynomials
in $z$ with complex coefficients. We show that the zeros of $P_n(z)$ which
satisfy $A(z)B(z)\neq 0$ lie on a real algebraic curve which we describe
explicitly.
