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If x^(2) +ax - 3x-(a+2) = 0 has real and...

If `x^(2) +ax - 3x-(a+2) = 0` has real and distinct roots, then minimum value of `(a^(2)+1)//(a^(2)+2)` is

A

1

B

0

C

`1/2`

D

`1/4`

Text Solution

Verified by Experts

The correct Answer is:
C
`D gt 0 rArr (a-3)^(2) +4(a+2) gt 0`
`rArr a^(2) -6a+9 +4a +8 gt0`
`rArr a^(2) +2a+17 gt 0`
`rArr a in R`
`:. (a^(2)+1)/(a^(2)+2) =1 -(1)/(a^(2)+2) ge (1)/(2)`
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