How many ordered pairs of solutions $(a,b)$ are there such that:

- $a$ is a root of the quadratic equation $y = x^2 + ax + b$
- $b$ is a root of the quadratic equation $y = x^2 + ax + b$

*Warning:* Think twice before you answer. If you didn't find any tricky part, then you probably got it wrong and should reconsider.