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  3. 3 recall that we say an element a is algebraic...

Question: 3 recall that we say an element a is algebraic...

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3. Recall that we say an element a is algebraic over a field F if it is the root of a polynomial in Flx (a) Prove that a V3 + V5 is algebraic over Q. (b) Find a basis for Q(a) over Q(5). What is (Q(a) :Q(V5)]? (c) Find a basis for (a over Q. What is Q(a Q? (d) Find the minimum polynomial for a over Q and prove it is irreducible (use pat (c)
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