Question

The function f(x)=x^4-3x^3-21x^2+kx+60, where k is a constant, has zeros at -1, -4, 3 and 5. What is the value of k?

Answer Choices:
A. -43
B. -37
C. 37
D. 43

Answer 1

Explanation:

The roots of the function (where it will be zero) are given as -1, -4, 3, and 5

Plug in one of the roots and set the equation to 0

f(-1)=((-1)^4)-(3(-1)^2)-(-21(-1)^2)+k(-1)+60

then

((-1)^4)-(3(-1)^2)-(-21(-1)^2)+k(-1)+60=0

because f(-1)=0 (the function at x=-1 will equal to 0

1+3-21-k+60=0

rearrange the equation

k=1+3-21+60

k=43

So the answer is Option D