Directly using "quest" as the root:
* Quest (noun) - a long or arduous search for something
* Questing (verb) - the act of searching for something
* Questor (noun) - someone who embarks on a quest
* Questorship (noun) - the office or position of a questor
Words derived from "quest" with slight variations:
* Inquest (noun) - a judicial inquiry, especially into a sudden, violent, or unexplained death
* Conquest (noun) - the act of conquering or taking control of a place or people
* Acquiesce (verb) - to accept something reluctantly but without protest (this one is a little more complex, as "quiesce" is closer to the root, but "quest" is still present)
Words related to the concept of a quest:
* Seek (verb) - to try to find something
* Search (verb) - to look for something carefully
* Explore (verb) - to travel through or examine a place or subject
* Investigate (verb) - to carefully examine the facts of a situation, crime, etc. to discover the truth
Remember that the root word "quest" can be used in different ways to create different meanings. You can use it as a direct root, add prefixes or suffixes, or use related words to explore the concept of searching for something.