Question

If f(x) = $a{x}^2$ + bx + c, then the value of a and b for which the identify f(x+1) - f(x) = 8x + 3 is satisfied, are

• A. a =1 and b = 4
• B. a = 1 and b = - 4
• C. a = 4 and b = 1
• D. a = 4 and b = -1

Answer 1

The correct option is D a = 4 and b = -1

We have, f(x + 1) - f (x) = 8x + 3
$\Rightarrow a(x+1{)}^2+b(x+1)+c-a{x}^2-bx-c=8x+3$
$\Rightarrow$ 2ax + a + b = 8x + 3
$\Rightarrow$ a = 4 and 4 + b - 3 = 0ie, b = -1
$\therefore$ The correct answer is (d)