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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 such that the quadratic equation `alphax^2-x+alpha=0` has two distinct real roots `x_1a n dx_2` satisfying the inequality `|x_1-x_2|<1.` Which of the following intervals is (are) a subset (s) of `S ?` `(1/2,1/(sqrt(5)))` b. `(1/(sqrt(5)),0)` c. `(0,1/(sqrt(5)))` d. `(1/(sqrt(5)),1/2)`

A

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

B

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

C

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

D

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

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The correct Answer is:
a,d
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