Read polynomial roots as intersection inputs

The curve $C$ has equation $y=\dfrac{x^2-2x+2}{x+1}$.

(i) Determine the asymptotes of $C$.

(ii) Sketch $C$, showing clearly any axial intercepts, turning points and asymptotes.

(iii) Deduce the number of real roots of the equation $x^4-2x^3+2x^2-x-1=0$.