The inequality y(-1)> -4 , y(1)< 0 , & y(3)> 5 are known to hold for y = ax² + bx + c then the least value of ‘a’ is:

(A) -1/4

(B) -1/3

(C) 1/4

(D) 1/8

Please write complete solution.

P

The inequality y(-1)>  -4 , y(1)< 0 , & y(3)> 5 are known to hold for y = ax² + bx + c then the  satisfy all the value and marks the eqns. given below:

Given that
y = ax^2 + bx + c
y(-1) > -4
therefore,

a*(-1)^2 + b(-1) + c > -4
a - b + c > -4 ..........................(i)

and
y(1) < 0
a + b + c < 0

or

-a -b -c > 0 ............................(ii)

and
y(3) > 5
9a + 3b +c > 5 .............................(iii)

Adding eq. (i) and eq. (iii)
10 a + 2b + 2c >1
i.e. 5 a + b + c > 0.5 .......................(iv)

Adding eq.s (ii) and (iv) we get,

4a > 0.5

8a > 1

thus, a > 1/8

(D) is the answer.

PLZ APPROVE!