Question 736102
Start with focusing on the zeros.  The complex with imaginary part needs also its conjugate.  Your simplest function is {{{x(x-1/2)(x-(1+i))(x-(1-i))}}}
={{{x(x-1/2)(x^2-2x+2)}}}.


When you let x=1, you find that the expression evaluation results in value of 1/2.  You want p(1)=2, which is an increase by a factor of 4, so you want {{{highlight(p(x)=4x(x-1/2)(x^2-2x+2))}}}
and you could fully multiply the expression into the polynomial if you want it in general form.