Q. The value of $b$ and $c$ for which the identify $f(x + 1) - f(x) = 8x + 3$ is satisfied, where $f(x) = bx^{2} + cx + d$, are
A) $b = 2,\ c = 1$
B) $b = 4,\ c = - 1$
C) $b = - 1,\ c = 4$
D) $b = - 1,\ c = 1$
Explanation
(b)
Since, $\left\lbrack b(x + 1)^{2} + c(x + 1) + d \right\rbrack - \left\lbrack bx^{2} + cx + d \right\rbrack - 8x + 3$
$\Rightarrow \ \ \ \ \ \ \ (2b)x + (b + c) = 8x + 3$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ 2b = 8,\ b + c = 3\ \Rightarrow b = 4,\ c = - 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.