Existence of a field extension such that for any natural number $n$ ,

Question

Let $K$ be a field, and $ f_1(x) , f_2(x) , \dots f_n(x) $ $\in$ $K[x]$ , such that deg $f_i(x)$ $\ge 1$ , $1\le i \le n $. I have to show that there exists a field extension $F/ K$ such that each $f_i(x)$ has a root in $F$.

I have no idea from where to start.

Any insight.Thank you.