A regular n-gon is constructible if and only if cos(2π/n) is constructible. (a) Prove that a regular hexagon is constructible. (b) Prove that a regular 7-gon is not constructible because cos(2π/7) is a root of the irreducible polynomial 8x³ + 4x² - 4x - 1.
A regular n-gon is constructible if and only if cos(2π/n) is constructible. (a) Prove that a regular hexagon is constructible. (b) Prove that a regular 7-gon is not constructible because cos(2π/7) is a root of the irreducible polynomial 8x³ + 4x² - 4x - 1.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 36E
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A regular n-gon is constructible if and only if cos(2π/n) is constructible. (a) Prove that a regular hexagon is constructible. (b) Prove that a regular 7-gon is not constructible because cos(2π/7) is a root of the irreducible polynomial 8x³ + 4x² - 4x - 1.
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