Troll Quadratic

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.

Source: BOGTRO from AoPS (I think).
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