The set of values of a for which ax² + (a - 2) x - 2 is negative for exactly two integral x, is

$\begin{array}{l}\mathrm{f}\left(\mathrm{x}\right)={\mathrm{ax}}^2+(\mathrm{a}-2)\mathrm{x}-2=(\mathrm{ax}-2)(\mathrm{x}+1)\\ \mathrm{f}\left(0\right)=-2\text{ and }\mathrm{f}(-1)=0\end{array}$

If a is negative then expression becomes negative for infinite values of x, therefore it must be positive. Expression to be negative for exactly two integral values of x

So $\frac{2}{\mathrm{a}}\le 2\text{ or }\mathrm{a}\ge 1$

and $\frac{2}{\mathrm{a}}>1\Rightarrow \mathrm{a}<2$

$\therefore \mathrm{a}\in [1,2)$