EDB — 0CB

Exercises

1. [0CB]Given $𝛼\ne 0$ and $p(x)=a_0+a_{1}x+\cdots +a_n{x}^n$, $p\in \mathbb{Q}[z]$ such that $p(𝛼)=0$, build a polynomial $q\in \mathbb{Q}[z]$ such that $q(1/𝛼)=0$.

   So if $𝛼\ne 0$ is algebraic then $1/𝛼$ is algebraic.

   Solution 1

   [0BR]↺↻