Proving an Isomorphism between $\mathbb{R} / (f) $ and $\mathbb{R} / (x^2) $

Question

$f= x^2 + bx + c \in \mathbb{R}[x]$. Given that the discriminant of $f$ is $0$ show the expression in the title holds. I have written $f$ as $$f = (x- \alpha)^2$$ where $\alpha$ is the repeated root of $f$. I am unsure of how to setup a homomorphism such that the kernel is $(f)$.