Question

the value if b and c for which the identity f(x+1) -f(x)=8x+3 is satisfied, where f(x) = bx^2 +cx +d are

Answer 1

$f(x + 1) - f(x) =$
$b{(x + 1)}^{2} + c(x + 1) + d - (b {x}^{2} + cx + d)$
$= 2bx + (b + c)$
$given \: 2bx + (b + c) = 8x + 3$
$i.e. \: b = 4 \: and \: c = - 1$

Answer 2

Answer:

The value of b and c are 4 and -1 respectively.

Step-by-step explanation:

Given the identity

$f(x+1)-f(x)=8x+3$

The value of b and c satisfied, where $f(x)=bx^2+cx+d$

$f(x+1)-f(x)=8x+3$

$b(x+1)^2+c(x+1)+d-bx^2-cx-d=8x+3$

$b(x^2+1+2x)+cx+c+d-bx^2-cx-d=8x+3$

$bx^2+b+2bx+cx+c+d-bx^2-cx-d=8x+3$

$b+2bx+c=8x+3$

$b+c+2bx=8x+3$

Comparing both sides

2b=8 ⇒ b=4

b+c=3 ⇒ 4+c=3 ⇒ c=-1

The value of b and c are 4 and -1 respectively.