The entire graph of the equation `y=x^2+k x-x+9` in strictly above the `x-a xi s` if and only if `k<7` (b) `-5-5` (d) none of these

Options

A. `k lt 7`
B. `-5 lt k lt 7`
C. `k gt -5`
D. None of these

Explanation

`y=x^(2) + (k-1)x+9= (x+ (k-1)/(2))^(2) + 9 - ((k-1)/(2))^(2)`
For the entire graph to be above the x-axis, we should have
`" "9- ((k-1)/(2))^(2) gt 0`
`rArr" "k^(2)-2k -35 lt 0 rArr (k=7)(k+5) lt 0`
`rArr -5 lt k lt 7`