Link between stationarity of AR(2) and stability condition of corresponding difference equation

In the standard textbooks, such as Hamilton (1994), it is stated that the conditions for stationarity of a process

$y_t = \theta_0 + \theta_1 y_{t-1} + \theta_1 y_{t-2} + \epsilon_t$

follow from the stability condition of the the characteristic equation of the corresponding difference equation

$(1-\theta_1 z - \theta_2 z^2) = 0$,

which are that its roots lie outside the unit circle.

I don't understand how the stability conditions of the corresponding difference equation relates to stationarity of an AR(2) process. Does anyone know a book or give me a hint on their relation?

Many thanks!

\begin{align} (1-\theta_1L-\theta_2L^2) y_t=e_t \end{align} where $L$ is the backward shift operator $(Ly_t=y_{t-1})$. Now convert the problem into an MA problem. \begin{align} y_t=\frac{1}{(1-\theta_1L-\theta_2L^2)} e_t \end{align} on the other hand assume that the polynomial, $(1-\theta_1L-\theta_2L^2)$ has two roots saying, $\alpha$ and $\beta$. Then you can write the denominator as, \begin{align} y_t=\frac{1}{(L-\alpha)(L-\beta)} e_t \end{align}
now rewrite each term in denominator as a power series, $\sum_{i=0}^{\infty}(L/\alpha)^i = \frac{-\alpha}{L-\alpha}$ and similarly for the second term. Now you can let the backward shift operator to operate on $e_t$ (before that L was in the denominator and there is no definition about how L can operate). But the point is that $\alpha$ and $\beta$ must be greater than one otherwise the power series diverges, meaning for example variance tends to infinity!
You should notice that $L$ is an operator not like a variable or parameter and it just operates linearly on the index of its next term.