Let f x = a x 2 + b x + c be such that f 1 = 3 , f - 2 = λ and f 3 = 4 . If f 0 + f 1 + f - 2 + f 3 = 14 , then λ is equal to

Step-by-step solution

Given f x = a x 2 + b x + c be such that f 1 = 3 ,   f - 2 = λ and f 3 = 4 . If f 0 + f 1 + f - 2 + f 3 = 14 , then λ is equal to Now given f 0 + f 1 + f - 2 + f 3 = 14 ⇒ f 0 + 3 + λ + 4 = 14 ⇒ f 0 = 7 - λ = c Now f 1 = a + b + c = 3         . . . i f 3 = 9 a + 3 b + c = 4             . . . ii f - 2 = 4 a - 2 b + c = λ             . . . iii Now subtracting equation ii - iii We get, a + b = 4 - &