I've been searching in bibliography about this test applied to an AR(p) model. $$Q(L)(Y_{t})=c+\epsilon_{t}$$
Where L represent the Lag Operator and $Q=1-\phi_{1}x-.....-\phi_{p}x^{p}$ is the polynomial expression associated to the model.
I know that if $Q(r)=0$ implies $|r|>1$, then the process is stationary (at least in weak sense).
My question is: Why the Null Hypothesis of Augmented Dickey-Fuller test is stated as: "$r=1$ is a root of the polynomial"? Rejecting that hypothesis implies that every single root of Q lies outside the unit circle??
I'm new at this area so every recommendation or suggestion will be useful. Thanks.