Let K be a field with char K 2,3 and consider the cubic equation x 3

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Let K be a field with char K ≠ 2,3 and consider the cubic equation x³+a₁x²+ a₂x+ a₃ = 0 (a_i ϵ K). Let p =

(with cube roots chosen properly). Then the solutions of the given equation are P + Q - a₁/3; wP + w²Q - a₁/3; and w²P + wQ - a₁/3 where w is a primitive cube root of unity.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 20, 2023 02:47 AM

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Let K be a field with char K 2,3 and consider the cubic equation x 3

Question:

=a2 - and q 3 2a₁³ a1a2 27 3 + a3.

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The given cubic equation is x3 a1x2 a2x a3 0 where ai K and char K 23 Let p a2 a123 and q 2a1327 a1a...View the full answer

Algebra Graduate Texts In Mathematics 73

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