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

If `x^2+a x-3x-(a+2)=0` has real and distinct roots, then the 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`
or `a^(2) - 6a + 9 + 4a + 8 gt 0`
or `a^(2) - 2a + 17 gt 0`
`rArr a in R`
`therefore (a^(2) + 1)/(a^(2) + 2) = 1 - (1)/(a^(2) + 2) ge 1/2`
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