Question

the function f(x) =kx^4+8x^2 has three turning points, a maximum value of 8 and a root at x=2. determine the value of k as well as the other zeros

Answer 1

Given:

The function is f(x) =kx^4+8x^2.

The function has zero at x = 2.

Step-by-step explanation:

The function has zero at x = 2, so f(2) = 0.

Determine the value of k by using f(2) = 0.

`\begin{gathered} f(2)=k(2)^4+8(2)^2 \\ 16k=-32 \\ k=-(32)/(16) \\ =-2 \end{gathered}`

So function is,

`f(x)=-2x^4+8x^2`

For the zeros of the function f(x) = 0. So,

`\begin{gathered} -2x^4+8x^2=0 \\ -2x^2(x^2-4)=0 \\ -2x^2(x-2)(x+2)=0 \\ x=0,2,-2 \end{gathered}`

So other roots of the function is 0 and -2.

Answer:

Value of k is -2

Other roots: 0 and -2