Algebra Level 5

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.

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