Question 869101
Complex roots always come in complex conjugate pairs. 
Since {{{4-i}}} is a root, then so is {{{4+i}}}}.
In order to have rational coefficients, you ned to have a difference of squares to eliminate the {{{sqrt(6)}}}.
{{{f(x)=(x-sqrt(6))(x+sqrt(6))(x-(4-i))(x-(4+i))}}}
{{{f(x)=(x^2-6)(x^2-8x+17)}}}
{{{f(x)=x^4-8x^3+11x^2+48x-102}}}