Question 966499


The polynomial


{{{f(x)}}} = {{{(x-4)}}}.{{{(x-i)}}}.{{{(x+i)}}}.{{{(x-(7+i))}}}.{{{(x-(7-i))}}} = {{{(x-4)}}}.{{{(x^2+1)}}}.[{{{(x-7)^2 + 1)}}}] 


has real coefficients,  the degree  5,  the root  4,  the root  -i,  and the root 7+i.