Option D Should be Correct
Alternate forms of equation:
Above equation has no real roots and if at least one of the root is of modulus one (which is both +1 and -1) as stated by question then it should be integer root of the equation.
Putting x= 1 in the main equation we get : c = - a - b - 2............(1)
Putting x= -1 in the main equation we get : c = - a + b + 2.............(2)
Adding (1) and (2) we get
2c = - 2a
c= -a
Correct me if wrong