Question

The value of b and c for which the identity f(x+1) - f(x) = 8x + 3 is satisfied, where $f\left(x\right)=b{x}^2+cx+d$ are

• A. b = 2, c = 1
• B. b = 4, c = –1
• C. b = – 1, c = 4
• D. b = – 1, c = 1

Answer 1

The correct option is B

b = 4, c = –1

$\because f(x+1)-f\left(x\right)=8x+3\Rightarrow \left\{b\right(x+1{)}^2+c(x+1)+d\}-\{b{x}^2+cx+d\}=8x+3\Rightarrow b\left\{\right(x+1{)}^2-x^2\}+c=8x+3\Rightarrow b(2x+1)+c=8x+3oncomparing$

2b = 8 and b + c = 3

Then, b = 4 and c = –1