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.
Thank you in advance

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 $-2B^2$.
