Which symptoms would I have if a root tip was left behind during extraction?

Usually no problems. It is sometimes recommended to leave the root than to risk damage to the nerve that can cause paresthesia and neuropathic pain. You are always informed by your dentist of the retained root tip.
It can vary. Whether or not a root tip that is left behind during an extraction becomes symptomatic or remains asymptomatic may depend on the size of the root tip, where the root tip is, and the reason why the tooth was removed. Leaving a root tip of an abscessed tooth is likely to become a problem if it is not removed. Leaving a small root tip of an asymptomatic wisdom tooth is less likely to be a problem.