# Stationarity of AR(2) process

I am new to time series modeling and currently struggling with stationarity. Can someone please explain why the roots of the following AR polynomial are $$- 1$$ and $$1/2$$?

The AR(2) process is $$X_t = X_{t-1} + 2 X_{t-2} + Z_t$$

To my best knowledge so far, I could use backward shift operator writing

$$(1- B + 2B^2)X_t = Z_t$$

But I don`t know how to proceed with that.

The shift operator $$1-B-2B^2$$ factorizes as such: $$1-B-2B^2=(1+B)(1-2B).$$
Note that in your question you had a sign error when writing down the shift operator - the $$2X_{t-2}$$ moves from the right to the left side of the equation and thus becomes a $$-2B^2$$.