Answer:
Option A,B,C
Explanation:
Given , x1 and x2 are roots of αx2−x+α=0
∴ x1+x2=1α and x1x2=1
Also, |x1−x2|<1
⇒ |x1−x2|2<1⇒(x1−x2)2<1
or (x1−x2)2−4x1x2<1
⇒ 1α2−4<1 or 1α2<5
⇒ 5α2−1>0
or (√5α−1)(√5α+1)>0

∴ αϵ(−∞,−1√5)∪(1√5,∞) ......(i)
Also, D>0
⇒ 1−4α2>0 or αϵ(−12,12) .....(ii)
From Eqs. (i) and (ii) , we get
αϵ(−12,−1√5)∪(1√5,12)