Show that $x^2 +1$ is irreducible in $\mathbb{R}[x]$, but it has roots in $\mathbb{R}[x]\space/\space(x^2 +1) \cong \mathbb{C}$
$\mathbb R[x]/\langle x^2+1\rangle\simeq\mathbb C$ and $\mathbb R[x]/\langle x^2+1\rangle$ contains a zero of $x^2+1$