3. * 6 pts. Let F= Q(T). • Explain why s = 12 +1 +1 is...

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Question

3. * 6 pts. Let F= Q(T). • Explain why s = 12 +1 +1 is algebraic over F. Determine Irr(5,F). • Determine Irr(, Q(T)) • Deter

Answer 1

Answer #1

Let p e Q[X] of degre d. Consider the field extension Q(7) Shall show this is an algebraic extension of degree d. Clearly 7 s

Using the above result we can say immediately Q(T) is algebraic over Q(1? + 1 + 1) of degree 2. Irr(2, Q(75)) = X5 - 75 Irr(,

Answer 2

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