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I EXAMPLE 8 The Splitting Field of x" – a over Q Let a be a positive rational number and let w be a primitive nth root of unity (see Example 2 in Chapter 16). Then each of all", wa", w²al", ..., o"-'ah is a zero of x" – a in Q(Va, w).

I EXAMPLE 8 The Splitting Field of x" – a over Q Let a be a positive rational number and let w be a primitive nth root of unity (see Example 2 in Chapter 16). Then each of all", wa", w²al", ..., o"-'ah is a zero of x" – a in Q(Va, w).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let F(a) be the field described in Exercise 8. Show that a2 and a2 + a are zeros of x3 + x + 1.

I EXAMPLE 8 The Splitting Field of x" – a over Q Let a be a positive rational number and let w be a primitive nth root of unity (see Example 2 in Chapter 16). Then each of all", wa", w²al", ..., o"-'ah is a zero of x" – a in Q(Va, w).
Transcribed Image Text:I EXAMPLE 8 The Splitting Field of x" – a over Q Let a be a positive rational number and let w be a primitive nth root of unity (see Example 2 in Chapter 16). Then each of all", wa", w²al", ..., o"-'ah is a zero of x" – a in Q(Va, w).
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