Share
Explore BrainMass

Find Irreducible Polynomial

Find an irreducible polynomial defining the extension Q(3^1/2, 5^1/2).

Attachments

Solution Preview

Let K=Q(sqrt(3),sqrt(5))
Degree of K:Q=4
Let a=sqrt(3)+sqrt(5) (1),

THEN we'll prove that K=Q(a)

We have:a^2= 8+2*sqrt(15)
a^4= 124+ 32*sqrt(15)=16*a^2-4 (from ...

Solution Summary

An irreducible polynomial defining an extension is found.

$2.19