Find the least value of `n` such that `(n-2)x^2+x+n+4>0,AAx in R ,w h e r en in Ndot`

Explanation

`(n-2)x^(2) + 8 x + n + 4 gt 0, AA x in `R
`rArr D = 64 - 4 (n- 2) (n + 4) lt 0 and n - 2 gt 0`
`rArr 16 - (n^(2) + 2n - 8) lt 0 and n gt 2`
`rArr n^(2) + 2n - 24 gt 0 and n gt 2`
`rArr (n + 6) (n - 4) gt 0 and n gt 2`
`rArr n gt 4 as n in N and n gt 2`
`rArr n ge 5`
Hence, the least value of n is 5.