# Homework Help: Given min. polynomial of a, find min. polynomial of 1/a

1. Dec 8, 2012

### ryou00730

1. The problem statement, all variables and given/known data
Given that the minimal polynomial of a over rationals is x^4+x+8, find the minimal polynomial for 1/a over Q.

2. Relevant equations
I know there is a lot of work done out there for finding the min. polynomials of a^k for k>0, however I've never seen anything with a^k for k<0. I have no intuition where to start with this problem, just wondering if there are methods out there.

2. Dec 8, 2012

### micromass

You know that

$$a^4+a+8=0$$

An obvious thing to do is to multiply both sides by $\frac{1}{a}$ multiple times.

3. Dec 8, 2012

### ryou00730

Yea I realized this soon after posting, thanks for the help anyway.