n=4; i and 5i are zeros; f(-1)=104

Question

I don’t know how to solve this

Answer 1

x=i

x^2 =-1

x^2+1 is one factor

x=5i

x^2 = -25

x^2 +25 = a 2nd factor

f(-1)=104 = a(x^2+1)(x^2+25)

104/a = ((-1)^2 +1)((-1)^2 +25) = 2(26)= 52

a = 104/52 = 2

a= 2

f(x) = 2(x^2+1)(x^2+25)

f(x) = 2(x^4 +26x^2 +25)

f(x) = 2x^4 +52x^2 +50

n=4 means 4 zeros

if i is a zero, so is -i

if 5i is a zero so is -5i

imaginary zeros come in conjugate pairs