Given:
The function is f(x) =kx^4+8x^2.
The function has zero at x = 2.
Explanation:
The function has zero at x = 2, so f(2) = 0.
Determine the value of k by using f(2) = 0.
[tex]\begin{gathered} f(2)=k(2)^4+8(2)^2 \\ 16k=-32 \\ k=-\frac{32}{16} \\ =-2 \end{gathered}[/tex]
So function is,
[tex]f(x)=-2x^4+8x^2[/tex]
For the zeros of the function f(x) = 0. So,
[tex]\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}[/tex]
So other roots of the function is 0 and -2.
Answer:
Value of k is -2
Other roots: 0 and -2
