EDB — 0CF

Exercises

1. [0CF]Difficulty:*.More generally, given \(p(x)=a_ 0+a_ 1x+\cdots + a_ n x^ n\), \(p∈ℚ[z]\) \(q(x)=b_ 0+b_ 1x+\cdots + b_ m x^ m\), \(q∈ℚ[z]\), and given \(𝛼,𝛽\) such that \(p(𝛼)=0=q(𝛽)\), construct a polynomial \(r∈ ℚ[z]\) such that \(r(𝛼+𝛽)=0\).

   (Hint. use the theory of the resultant [ 35 ] ).

   So if \(𝛼,𝛽\) are algebraic then \(𝛼+𝛽\) is algebraic.

   Solution 1

   [0CG]↺↻