find the minimal positive eigenvalue satisfying (A+tB)v=0

Question

Given conditions:

1. matrix $A$ is symmetric and positive definite

2. matrix $B$ is symmetric and NOT positive definite

3. $0\leq t$

then linear system $$(A+tB)x=y$$

has solution for $0\leq t<\bar t$, where $\bar t$ represents the the minimal positive eigenvalue of the problem: $$ (A+tB)v=0 $$

How to calcuate the value of $ \bar t$?