Question

Given f ( x ) = 3 x 2 + k x − 13 f(x)=3x 2 +kx−13, and the remainder when f ( x ) f(x) is divided by x + 4 x+4 is 15 15, then what is the value of k k?

Answer 1

Answer:

k=5

Step-by-step explanation:

We are provided with function, f ( x ) = 3 $x^{2}$ + kx − 13

which is divided by x+4 gives 15.

Here,

since f(x) is divided by x+4 so we can put :

x+4 = 0

x= -4

Putting this in f(x) -----> f(-4)

f(x) = f(-4) = 3 ($-4^{2}$) + k(-4) − 13

f(-4) = 3(16) - 4k - 13

f (-4) = 48 - 4k - 13                ------------------------------------------Equation 1

Since, when f(x) is divided by x+4 , the remainder is 15 so we can say,

f(-4) = 15

putting in equation 1

f (-4) = 15 = 48 - 4k - 13

48 -4k - 13 = 15

35 - 4k = 15                      

35 - 15 = 4k                         (Moving - 4k on right hand side and 15 on the left)

or 20 = 4k

or 4k = 20

k = $\frac{20}{4}$

k = 5