Compute the number of ordered pairs $(a,b)$ of integers such that the polynomials $x^2 - ax + 24$ and $x^2 - bx + 36$ have one root in common.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Compute the number of ordered pairs $(a,b)$ of integers such that the polynomials $x^2 - ax + 24$ and $x^2 - bx + 36$ have one root in common.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
12
Compute the number of ordered pairs $(a,b)$ of integers such that the polynomials $x^2 - ax + 24$ and $x^2 - bx + 36$ have one root in common.
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