greater than, equal to or less than zero

I'm not sure this is the right forum, but here goes:

Depending on $\displaystyle \alpha \in \mathbb{R}$, find where the expression

$\displaystyle (xy)^2 + (\alpha + x)y^2$ is greater than zero, less than zero and equal to zero.

I suppose the first step is to write it as

$\displaystyle y^2 (x^2+x+\alpha)$.

So, if $\displaystyle y=0$, than the expression is zero, no matter what the $\displaystyle \alpha$ is.

Also, if $\displaystyle y>0$ or $\displaystyle y<0$, $\displaystyle y^2>0$, so it comes down to whether $\displaystyle x^2+x+\alpha$ is 0, <0 or >0.

I've tried and tried, but no luck.

Please, help.