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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!
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