Answer:
The value of a = -2.
The value of the zeros are -2, +2, 0.
Step-by-step explanation:
Let's first calculate the value of a, knowing that there is a zero at x =2 (meaning that f(2)=0):
[tex]f(x)=ax^{4} + 8x^{2}\\f(2)=a(2)^{4} + 8(2)^{2}=0\\16a+32=0\\16a=-32\\a=-2[/tex]
The function now looks like this: [tex]f(x)=-2x^{4} + 8x^{2}[/tex]
In order to find the other zeros, let's factorize:
[tex]f(x)=-2x^{4} + 8x^{2}\\f(x)=-2*(x^{2})*(x^{2} - 4)\\f(x)=-2*(x^{2})*(x-2)*(x+2)\\[/tex]
So the value of the zeros are -2, +2, 0.
