The biggest whole number that is a solution of $x^2+(\sqrt3-\sqrt2)x-\sqrt6>0$

Question

I should find the biggest whole number that is a solution of $x^2+(\sqrt3-\sqrt2)x-\sqrt6>0$.

We can find that the discriminant $D=(\sqrt2+\sqrt3)^2$ and the roots are $x_1=-\sqrt3$ and $x_2=\sqrt2$. So I think the solutions are $x\in (-\infty;-\sqrt3)\cup(\sqrt2;+\infty)$. What answer should I give? $0$ is a whole number, right?

Answer 1

Since the question asks for the biggest whole number, yet the solution set includes an interval stretching to $+\infty$, you should say there is no biggest whole number that satisfies the inequality.