Describe primary radicals of $R[x]$

Question

Let $rad$ - intersection of primary ideals of $R[x]$.

$rad(M_n(R)) = M_n(rad(R)), 1 \in R$

$rad(R[x]) = ?$

I suppose that $rad(R[x]) = (rad(R))[x]$. But is it correct to say that $rad$ is nilradical?