FunctionMedium
Question
The value of b and c for which the identity f ( x + 1) - f (x) = 8x + 3 is satisfied, where f(x) = bx2 + cx + d, are -
Options
A.b = 2, c = 1
B.b = 4, c = - 1
C.b = - 1, c = 4
D.b = - 1, c = 1
Solution
f(x + 1) - f(x) = 8x + 3
f(0 + 1) - f(0) = 3 (put x = 0)
⇒ (b + c + d) - d = 3
⇒ b + c = 3 ...........(i)
Also f (-1 + 1) - f (-1) = -8 + 3 (put x = -1)
⇒ f (0) - f (-1) = -5 ⇒ d - (b - c + d) = -5
⇒ - b + c = -5 ..........(ii)
from (i) and (ii)
b = 4, c = - 1
f(0 + 1) - f(0) = 3 (put x = 0)
⇒ (b + c + d) - d = 3
⇒ b + c = 3 ...........(i)
Also f (-1 + 1) - f (-1) = -8 + 3 (put x = -1)
⇒ f (0) - f (-1) = -5 ⇒ d - (b - c + d) = -5
⇒ - b + c = -5 ..........(ii)
from (i) and (ii)
b = 4, c = - 1
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