Find the nth-degree

Question

n=4

i and 4i are zeros

f(-1)=102

f(x)=

Answer 1

If i and 4i are zeroes, then conjugates, -i and -4i are zeroes as well

So

f(x)=a(x-i)(x+i)(x-4i)(x+4i)=a(x²+1)(x²+16)

Since f(-1)=102,  therefore

a(2)(17)=102

a=3.

So 

f(x)=2(x²+1)(x²+16)