Anyone on here who knows laplace transforms? I've been stuck for like 3 hours here

I got the transform 1/(s^2 - 3) which means we have poles on s = +-sqrt(3), but what exactly does this mean? I know that if you have a pole on the right side of the complex plain then you have something that is exponentially increasing, and if you have a pole on the left side it's exponentially decaying. But what happens when you have both? 😳