If `f(x)=ax^(2)+bx+c` and `f(-1) ge -4`, `f(1) le 0` and `f(3) ge 5`, then the least value of `a` is

Options

A. A. `1//4`
B. B. `1//8`
C. C. `1//3`
D. D. `-1//3`

Answer

B

Explanation

`(b)` `f(-1) ge -4`
`implies a-b+c ge -4`………`(i)`
`f(1) le 0`
`implies a+b+c le 0`
`implies -a-b-c ge 0`………`(ii)`
`f(3) ge 5`
and `9a+3b+c ge 5`……….`(iii)`
From `(i)+(ii) implies -2b ge -4`…….`(iv)`
From `(ii)+(iii)+(iv) implies 8a ge 1 implies age 1//8`