Let S be the set of all non-zero real numbers such that the quadratic equation alpha x^2-x+alpha =0 has two distinct real roots x_1  and x_2  satisfying the inequality |x_1-x_2|lt 1.  Which of the following intervals is(are) a subset(s) of S) （ ） A . (-frac 1 2,-frac 1(sqrt 5)) B . (-frac 1(sqrt 5),0) C . (0,frac 1(sqrt 5)) D . (frac 1(sqrt 5),frac 1 2)

AD Take the square root on both sides. Eq Also Eq From ( 1 ) and ( 2 ) The options A and D are correct.