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If f(x)=ax^(2)+bx+c and f(-1) ge -4, f(1...

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

A

`1//4`

B

`1//8`

C

`1//3`

D

`-1//3`

Text Solution

Verified by Experts

The correct Answer is:
B
`(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`
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