An algebra problem by Ajay Dutta

Algebra Level 2

For two sets \[A=\{(x,y) \mid y=x^2-ax+48\}, B=\{(x,y) \mid y=0\},\] what is the minimum value of a positive integer \(a\) that satisfies \(n(A \cap B)=2?\)

Note: \(n(X)\) is the number of the elements of the set \(X.\)

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