be a field and let f(x) = F be of degree n > 1. Let K be an extension field of F a

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 23E
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Let F be a field and let f(x) = F be of degree n ≥ 1. Let K be an extension field of F and
A₁, A2, A3.... Ar in K be disticcnt roots of f(x) in K > . Let m; be the order of root ai,
i = 1, 2, 3,... r. Then
n > M₁ + M₂ + + m₂ > r
Transcribed Image Text:Let F be a field and let f(x) = F be of degree n ≥ 1. Let K be an extension field of F and A₁, A2, A3.... Ar in K be disticcnt roots of f(x) in K > . Let m; be the order of root ai, i = 1, 2, 3,... r. Then n > M₁ + M₂ + + m₂ > r
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