(a) Show that Q(√3, i) is a simple exension of Q by verifying that Q(√3, i) = Q(√3+ i). (b) Show that Q(√3, i) is the splitting field for x² – 2x² – 3 over Q.
(a) Show that Q(√3, i) is a simple exension of Q by verifying that Q(√3, i) = Q(√3+ i). (b) Show that Q(√3, i) is the splitting field for x² – 2x² – 3 over Q.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(a) Show that Q(√3, i) is a simple exension of Q by verifying that Q(√3, i) = Q(√3+ i).
2x² - 3 over Q.
(b) Show that Q(√3, i) is the splitting field for x4 - 2x²
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