Understanding the definition of a polynomial over an arbitrary commutative unitary finite Ring R to understand REDEI RATIONAL FUNCTIONS

Question

I'm reading a paper that introduce a fast evaluation algorithm for Redei functions.

In the Introduction:

Let $R$ an arbitrary commutative unitary finite Ring and let $t(x) = x^2 - ax - b$ denote a polynomial over R with the two different roots $\alpha$, $\overline{\alpha}$.

I understand the definition of an arbitrary commutative unitary finite Ring.

I know that $\mathbb{{Z} _{n}^{*}}$ is commutative unitary finite Ring but I don't know how to relate the polynomial $t(x)$.

Link, if the paper is needed

What is the relation between this polynomial $t(x)$ and $\mathbb{{Z} _{n}^{*}}$ ?

Thanks.