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Show that u = √3+ √2i is algebraic over Q and type its minimal polynomial p(x) = irr(u, Q) below.

Show that u = √3+ √2i is algebraic over Q and type its minimal polynomial p(x) = irr(u, Q) below.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The polynomial f = x³ - 4x + 2 is irreducible over Q. Let u be a root of f in some extension Q(u) of Q. Compute for (1+2u) (1-u²). Enter your answer 5 Show that u = √3+ √2i is algebraic over Q and type its minimal polynomial p(x) = irr(u, Q) below. Enter your answer 6 List down the elements enclosed in a pair of braces {}.( ( Find a basis for Q(√2, √6 + √10) over Q(√3+ √5).
Transcribed Image Text:The polynomial f = x³ - 4x + 2 is irreducible over Q. Let u be a root of f in some extension Q(u) of Q. Compute for (1+2u) (1-u²). Enter your answer 5 Show that u = √3+ √2i is algebraic over Q and type its minimal polynomial p(x) = irr(u, Q) below. Enter your answer 6 List down the elements enclosed in a pair of braces {}.( ( Find a basis for Q(√2, √6 + √10) over Q(√3+ √5).
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