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If $f:Z\rightarrow Z $ is defined as $f(x)=x^2+ax+b$ then the values of $a$ and $b$ are ?

$\begin{array}{1 1}a\in Z,\:\:b\in Q-Z \\ a,b \in Z \\ b\in Z,\:\:a\in Q-Z \\a,b\in Q-Z \end{array}$

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