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If the quadratic equation x^(2)-36x+lamb...

If the quadratic equation `x^(2)-36x+lambda=0` has roots `alpha` and `beta` such that `alpha`, `beta in N` and `(lambda)/(5) cancel in Z` and `lambda` assumes minimum possible value then `(sqrt(alpha+2)sqrt(beta+2))/(|alpha-beta|)` is equal to

A

`(3)/(8)`

B

`(3)/(16)`

C

`(sqrt(111))/(34)`

D

`(sqrt(111))/(17)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(a)` `x^(2)-36x+lambda=0`
`:. Lambda=36x-x^(2)`
`alpha=1`, `lambda=5`, `beta=35` (rejected)

`:.alpha=2`, `lambda=68`, `beta=34` or `alpha=34`, `beta=2`
`:. (sqrt(36)sqrt(4))/(32)=(3)/(8)`
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