EDB — 0CB

Exercises

1. [0CB]Given \(𝛼≠ 0\) and \(p(x)=a_ 0+a_ 1x+\cdots + a_ n x^ n\), \(p∈ℚ[z]\) such that \(p(𝛼)=0\), build a polynomial \(q∈ℚ[z]\) such that \(q(1/𝛼)=0\).

   So if \(𝛼≠ 0\) is algebraic then \(1/𝛼\) is algebraic.

   Solution 1

   [0BR]↺↻