Proving an Algebraic Number: Root 3 + Root 2

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SUMMARY

The discussion focuses on proving that the expression Root 3 + Root 2 is an algebraic number. Specifically, it highlights the need to express this number in the form of a polynomial equation with integer coefficients. An example provided is the polynomial for Root 2, which is 1 * (Root 2)^2 + 0 * (Root 2)^1 - 2 * (Root 2)^0. The participants emphasize the importance of demonstrating that not all coefficients are zero, confirming the algebraic nature of the number.

PREREQUISITES
  • Understanding of algebraic numbers and their definitions
  • Familiarity with polynomial equations and their coefficients
  • Basic knowledge of square roots and their properties
  • Experience with linear algebra concepts
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  • Research how to construct polynomial equations for algebraic numbers
  • Learn about the properties of algebraic numbers and their classifications
  • Study examples of proving algebraic numbers using polynomial forms
  • Explore the relationship between algebraic numbers and field extensions
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Students and educators in mathematics, particularly those studying algebra and linear algebra, as well as anyone interested in the properties of algebraic numbers.

lokisapocalypse
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I need to show that this is an algebraic number.

In other words,

I need to show: an*x^n + an1*x^(n-1) + ... + a1 * x^1 + a0 * x^0 =
where the a terms are not ALL 0 but some of them can be.

Like for root 2 by itself,

I have 1 * (root 2) ^ 2 + 0 * (root 2)^1 + -2 * (root 2) ^ 0
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