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Let S be the set of all non-zero real nu...

Let S be the set of all non-zero real numbers `alpha` such that the quadratic equation `alphax^2-x+alpha=0` has two distinct real roots `x_1` and `x_2` satisfying the inequality `abs(x_1-x_2)lt1`. Which of the following intervals is (are) a subset(s) of S ?

A

`(-1/2,-1/sqrt5)`

B

`(-1/sqrt5,0)`

C

`(0,1/sqrt5)`

D

`(1/sqrt5,-1/2)`

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The correct Answer is:
A, D
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