$R=\mathbb{Z}[x]$ - polynomials with integer coefficients
$I = (x^2+x-1)\mathbb{Z}[x]$
In this case we have that classes of factor-ring $R/I$ represented in the next form: $K_{a,b}=ax+b$.
What ring is isomorphic to factor-ring $R/I$? I have suggestion that it will be $\mathbb{R}$, but I'm not sure and can't prove this.
All answers are highly appreciated. Thank you in advance.
Hint:
Put $\;\phi:=\frac{1+\sqrt5}2\;$ , and define
$$f:\;\Bbb Z[x]\to\Bbb Z[\phi]\;,\;\;f(p(x)):=p(\phi)$$
Show the above is an epimorphism of rings. What's $\;\ker f\;$ ? How in the world did I come up with that particular $\;\phi\;$ ?!