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snazy20
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Homework Statement
Let f = ax^3+bx^2+cx+d in R[x] be a cubic polynomial with real coefficients (a not equal to 0). Let g,h,k in Complex Numbers be roots of f. Let Af = R[x]/(f).
Prove that there are exactly 4 non-isomorphic algebras among algebras Af.
The Attempt at a Solution
Proved f either has 1 real and 2 distinct complex nonreal roots or 3 real roots. In the former case some of roots can coincide (3 or 2 or none).
From here I have become stumped, completely. Hope I have given enough for some help - please let me know if anything is unclear, but I have no idea where to go.
Thanks in advance