Question

Consider the inequation `x^(2) + x + a - 9 lt 0`
The value of the parameter a so that the given inequaiton is ture `AA x in (-1,3)`
A. `(-oo,-3]`
B. `(-3,oo)`
C. `[9,oo)`
D. `(-oo, 34//4)`

Answer 1

Correct Answer - 1
If `x^(2)+ x + a-9 lt 0` is ture `AA x in (-1,3)`, then `f(-1) lt 0 and f(3)lt 0`
`therefore 1-1 + a -9 lt 0 and 9 + 3 + a-9 lt 0`
`rArr a lt 9 and a le -3`
`rArr a le - 3`