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The value of alpha, for which the equati...

The value of `alpha`, for which the equation `x^2-(sinalpha-2)x-(1+sinalpha)=0` has root whose sum of square is least, is

A

`pi//4`

B

`pi//3`

C

`pi//2`

D

`pi//6`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Let `p`, `q` are roots.
`p^(2)+q^(2)=(p+q)^(2)-2pq`
`=(sinalpha-2)^(2)+2(1+sin alpha)`
`=(sin alpha-1)^(2)=5`
For least value `sin alpha=1`
`implies alpha=pi//2`
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