Find the minimal polynomial over QQ and RR for ... root(3)(3),1-isqrt3, 2+i, i root(3)(3)

Matonya

Matonya

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2022-08-16

Find the minimal polynomial over Q and R for ... 3 3 , 1 i 3 , i 3 3

Answer & Explanation

kunstboom8w

kunstboom8w

Beginner2022-08-17Added 8 answers

Let α = 3 3
Let's get rid of that pesky radical by cubing both sides:
α 3 = 3
Then move 3 over to the other side:
α 3 3 = 0
Let f = x 3 3. Now f is irreducible in Q [ x ] by Eisenstein's Criterion (p=3) and Gauss' lemma. So the minimal polynomial for 3 3 over Q is m 3 3 = x 3 3
The rest follow a very similar procedure.

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