Unit root/ Random walk

Please correct me if i’m wrong.
A model has unit root if the t stat for b1 is significant, (b1 not equal to 0).
But if b1 and b0 are not significant (b1=b0=0), we say that the model doesn’t have unit root. In this case, how does the model predict results if both coefficients are = 0? isn’t this random walk?

A time series has stationarity if a shift in time doesn’t cause a change in the shape of the distribution; unit roots are one cause for non-stationarity.
All covariance-stationary time-series have a finite mean-reverting level, which is E(xt)=b0/(1-b1). If b1=1, then E(xt) doesn’t exist. That is random walk. By the way, if b0≠0 then it’s a random walk with drift.

If b1 = 0 the model is not working there is no preduction

X(t) = 0 x X(t-1) + error

The model does not have any use

Unit root is issue
b1 = 1
X(t) = 1 x X(t-1) + Error
best estimate of this times value is last times plus a rangom number - not much use as a model either.

Not if B1 = 1 than doing a t-test on b1 will not work and we need to do first differencing and a dicker fuller test.