Consider the inequation `x^(2) + x + a - 9 lt 0`
The values of the real parameter a so that the given inequaiton has at least one positive solution:

Options

A. `(-oo,37//4)`
B. `(-oo,oo)`
C. `(3,oo)`
D. `(-oo,9)`

Answer

4

Explanation

Let `f(x) = x^(2) + x + a-9`
`x^(2) + x + a- 9 gt 0` has at least one positve solution, the either both the roots of equation `x^(2) + x + a-9=0` are non-negative or 0 lies betweens the roots.

Now sum of roots `= -(1)/(2)`, hence, case I is not possible . For Case II, `f(0) lt 0 rArr a-9 lt 0 or a lt 9`