Zeteo (which we pronounce zeh-TAY-o) is a transliteration of a Greek verb (ζητέω) used liberally in classical Greek philosophy as well as in the New Testament.  The verb may be translated: to challenge, to question, to seek honestly, to dispute, to debate and pose alternative ideas and solutions. See, for example, Matthew 7:7:

Ask and it will be given to you; seek (zeteo) and you will find; knock and the door will be opened to you. For everyone who asks receives; he who seeks (zeteo) finds; and to him who knocks, the door will be opened.

Zeteo! Reading, Looking, Listening . . . Questioning.