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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