Say I have some number field $K_1/\mathbb{Q}$ defined as: $$K_1 \cong \mathbb{Q}[x]/\langle f(x)\rangle$$ for some irreducible (monic, if this makes things easier) polynomial $f(x)$. Now, let $g(x)\in K_1[x]$ be an irreducible (monic) polynomial over $K_1$. I can then define the relative field extension $K_2$ as: $$K_2\cong K_1[x]/\langle g(x)\rangle$$
Now, $K_2/K_1/\mathbb{Q}$ is a tower of field extensions, but we can view $K_2/\mathbb{Q}$ directly as a number field. How can I go about finding the defining polynomial of $K_2$ over $\mathbb{Q}$? By this, I mean the irreducible (monic) polynomial $h(x)\in\mathbb{Q}[x]$ such that: $$K_2\cong \mathbb{Q}[x]/\langle h(x)\rangle$$