Can I find supremum of $(ax^2+bx+c)/x^2$ for non-zero $a, b, c$? Is there any condition for the function to converge?

Question

Actually I think I am wrong. I am trying to find,

$$\sup \limits_x \frac{{a{x^2} + bx + c}}{{{x^2}}}$$

I know that the above function is undefined at $x\to0$. I know I cannot use L'hospital rule here. Is there any condition that will make the objective function converge at $x \to 0$?