True of False. Explain. Let α ∈ C be algebraic over Q of degree n. If f (α) = 0 for nonzero f (x) ∈ R[x], then (degree f(x)) ≥ n. C = Complex numbers Q = Rational numbers R = Real numbers

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.4: Fractional Expressions
Problem 62E
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True of False. Explain.

Let α ∈ C be algebraic over Q of degree n. If f (α) = 0 for nonzero f (x) ∈ R[x], then (degree f(x)) ≥ n.

C = Complex numbers

Q = Rational numbers

R = Real numbers

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