"seek answers" is correct and can be used in written English. You can use it whenever you need to express the idea of looking for answers or information. For example: I decided to seek answers on the internet for my research paper.
Men seek answers.
Now his family will seek answers post-mortem.
Instead Pardew will now "seek answers" from Kinnear.
I can imagine her students loving her or equally not understanding her as they seek answers.
Courts are sometimes obliged to seek answers to questions about love that may well be unanswerable.
Over the next two weeks, they will seek answers for you.
Yet they no longer seek answers in the Helen Hills Hills Chapel (yes, Hills Hills).
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.