The phrase "a determined quest" is correct and usable in written English.
It can be used to describe a focused and resolute pursuit of a goal or objective.
Example: "Her journey was not just a vacation; it was a determined quest to find her roots and understand her family's history."
Alternatives: "an unwavering pursuit" or "a steadfast journey".
The struggle of the Middle East during the past century was a determined quest to exempt itself from great-power rivalry and superpower dominance.
It would be insulting to suggest of distinguished laureates, who have spent a lifetime in a determined quest for knowledge or excellence, that the principal value of a Nobel prize is monetary.
Since then, we've been on a determined quest to televisually de-evolve to a point where the next big reality TV series is likely to be a timelapse of some puddles in a derelict bin factory.
She's a death scholar of sorts, on a determined quest to honor forgotten victims of this city's defining natural disaster.
After the raid came riots, and after the riots came a more determined quest by L.G.B.T.
An intense new sci-fi short from filmmaker Luke Gilford follows a woman's determined quest "to feel connected to anything, something".
In Saram-ŭi Adeŭl (1979; Son of Man), he explored numerous Western and East Asian theologies in the course of tracing a young man's determined quest for transcendence.
There is a rare purity to the story of Christopher McCandless, the subject of biographical drama Into the Wild, whose determined quest to find a life less ordinary led ultimately to an agonisingly slow death from poisoning and starvation in the Alaskan wilderness.
News reporting is all about the determined quest for facts and ideas that originate elsewhere.
It's no insult to call the movie "old-school": one of the prime aspects of the modern cinema is backstory, the sense that a person's past is a determining element of his dramatic quest and the sympathies aroused.
The official involved in the Balco case said that investigators were trying to determine whether Quest's sports-testing division was an unwitting or complicit participant in possible pretesting of Balco athletes.
