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

f(x)=ax2+(a−2)x−2=(ax−2)(x+1)f(0)=−2 and f(−1)=0If 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 xSo 2a≤2 or a≥1and 2a>1⇒a<2∴ a∈[1,2)