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If the difference between the roots of the equation `x^2+""a x""+""1""=""0` is less than `sqrt(5)` , then the set of possible values of a is (1) `(-3,""3)` (2) `(-3,oo)` (3) `(3,oo)` (4) `(-oo,-3)`

A

`(0,1)`

B

`(-1, 1) - {0}`

C

`(-1, 0)`

D

`[-1, 1]`

Text Solution

Verified by Experts

The correct Answer is:
A
`2 cos^(-1) x = cot^(-1) ((2x^(2) -1)/(2x sqrt(1 -x^(2))))`
Put `x = cos theta : L.H.S. = 2 theta, 0 le theta le pi`
and `-1 le x le 1`...(i)
`R.H.S. = cot^(-1) ((cos 2 theta)/(2 cos theta|sin theta|)) = cot^(-1) (cot 2 theta) = 2 theta`
if `0 lt 2 theta le pi`...(ii)
From Eqs. (i) and (ii) , we get `0 lt theta lt pi//2`. Thus,
`x in (0, 1)`
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