# Common Roots

Algebra Level 5

How many ordered pairs of integers $$(a, b)$$ are there such that $$-61 \leq a \leq 61$$ and $$-61 \leq b \leq 61$$ and they satisfy the condition that $$x^2 + ax + b$$ and $$b x^2 + a x + 1$$ have a common (possibly complex) root?

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