Troll Quadratic

Algebra Level 5

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

  • a a is a root of the quadratic equation y=x2+ax+b y = x^2 + ax + b
  • b b is a root of the quadratic equation y=x2+ax+b 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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