Roots of $x^6+tx^3+t$ in $\mathbb{F}_3(t)[x]$

Question

I am trying to figure out what the roots are for a $x^6+tx^3+t$ in $\mathbb{F}_3(t)[x]$. The hint given is that the roots of this polynomial are "related to roots of a qudratic polynomial".

I am not even sure to approach this polynomials, looking for some pointers. I am not sure if the quadratic polynomial I should consider is just $x^2+tx^+t$ or something, although I am not sure how I can even justify that in the first place.

Answer 1

Hint: Substitute $$x^3=z$$ then you will get $$z^2+tz+t$$