to seek out
ekzeteo describes actively searching for God or something desired, and in passive clauses being required from a generation.
The attested use most often describes active pursuit: prophets search concerning salvation, people seek the Lord or God, and an individual seeks a desired outcome. In two passive clauses, it describes blood being required from a generation.
Senses in use
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Active pursuit of God or a desired outcome · dominant
In 1 Peter 1:10 the aorist active plural form concerns prophets searching and inquiring about the salvation and grace of which they prophesied. Acts 15:17 and Romans 3:11 place active forms with seeking the Lord or God, while Hebrews 11:6 speaks of those who seek him and Hebrews 12:17 of someone seeking repentance with tears.
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Being required from a generation · occasional
In Luke 11:50 the aorist passive subjunctive occurs in the clause about the blood of all the prophets being required of that generation. Luke 11:51 uses a future passive form for the blood of Abel through Zechariah; the APB renders the clause, "it will be sought out from this generation."
In the Anselm Project Bible: The APB commonly presents the active clauses with "seek" or "searched," and in Hebrews 12:17 adds "sought it with tears." In the passive clauses it uses "required" and "sought out"; these are verse-level renderings rather than fixed word alignments.