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

Let S be the set of the non zero real numbers `alpha` such that the quadratic equation `alphax^(2)-x+alpha=0` has two distinct real roots `x_(1)andx_(2)` satisfying the inequlity `|x_(1)-x_(2)|lt1` . Which of the following intervals is (are) a subset (s) of s?

A

`(-(1)/(2),-(1)/sqrt(5))`

B

`(-(1)/sqrt(5),0)`

C

`(0,-(1)/sqrt(5))`

D

`((1)/sqrt(5),(1)/(2))`

Text Solution

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The correct Answer is:
A, D
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