Math problem solve

Question

Let y= f (x) be a cubic quartic (Fourth degree) polynomial with leading coefficient a=1 and f(i)=f(2i)=0 Write an equation for F

Answer 1

x=i

x^2 =-1

x^+1 =0

x=2i

x^2 =-4

x^2+4 =0

F(x)=(x^2+1)(x^2+4)= x^4 +5x^2 +5