究 is a bound morpheme (b.f.) — it cannot be used alone as a standalone word. It appears in compound words where it carries two distinct meanings. In words like 研究 (research), 追究 (to investigate), and 查究 (to inquire into), it means 'to investigate or study carefully'. In the word 究竟 (after all, actually), it combines with 竟 to create an adverb meaning 'in the end' or 'when all is said and done'. When you encounter 究 in a new compound, the meaning is usually the investigative one.