Given min. polynomial of a, find min. polynomial of 1/a

[ryou00730]

Homework Statement

Given that the minimal polynomial of a over rationals is x^4+x+8, find the minimal polynomial for 1/a over Q.

Homework 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.

 

[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.

 

[ryou00730]

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