The correct option is D one root in (−∞,a) and other in (b,∞)
Let f(x)=(x−a)(x−b)−1
f(a)=−1 which is negative.
f(b)=−1 this is also negative.
Therefore, roots do not lie between a and b.
Thus, one root in (−∞,a) and other root lies in (b,∞).
Hence, option 'D' is correct.