Question 378946
Complex roots always come in complex conjugate pairs.
Since {{{x=3+i}}} is a solution, {{{x=3-i}}} is also a solution.
Since {{{x=i}}} is a solution, {{{x=-i}}} is also a solution.
{{{f(x)=(x-i)(x+i)(x-(3+i))(x-(3-i))}}}
{{{f(x)=(x^2+1)(x^2-6x+10)}}}
{{{f(x)=x^4-6x^3+11x^2-6x+10}}}