18-11-2022
Mathematics

Answered

Given f(x)=3x^2+kx+4 and the remainder when f(x) is divided by x-4 is 68 then What is the value of k?

Answer :

mhanifa mhanifa

19-11-2022

Answer:

k = 4

-----------------------------

Given

Function f(x) = 3x² + kx + 4,
Remainder of f(x) / (x - 4) is 68.

According to the remainder theorem, if we subtract 68 from the given trinomial it should be divisible by x - 4. In other words, one of zero's will be x = 4.

f(x) = 3x² + kx + 4 - 68 = 3x² + kx - 64 = 0

When x = 4

3*4² + k*4 - 64 = 0
48 + 4k - 64 = 0
4k - 16 = 0
4k = 16
k = 4

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