Hi,

I post the answer for 1) :

Since we have to find a 4th degree polynomial function w/ real coefficients

and i itīs a zero then -i itīz a zero too

Zeros are: -2,-1/2,i and -i

f(x)=a(x+2)(x+1/2)(x-i)(x+i) = a(x+2)(x+1/2)(x^2+1)

f(1)=a(3)(3/2)(2)=9a = 18

Then a = 2

Answer: 2(x+2)(x+1/2)(x^2+1)