The function \(f\) is defined by \(f(x) = \frac{x^2 + ax + b}{2x + c}…

Question

Prompt

The function

f

is defined by

f (x) = \frac{x ^{2} + a x + b}{2 x + c}

, where

a

b

, and

c

are constants. The graph of the function

f

in the xy-plane, where

y = f (x)

, does not intersect the line

x = 4

. If

f (5) = f (6) = 0

, what is the value of

a + b + c