Question 1071910
Real coefficients in a polynomial with complex roots means the roots come in complex conjugate pairs,
{{{f(x)=a(x-(1+i))(x-(1-i))(x-i)(x+i)}}}
{{{f(x)=a(x^2-2x+2)(x^2+1)}}}
{{{f(x)=a(x^4-2x^3+3x^2-2x+2)}}}
So then,
{{{2a=6}}}
{{{a=3}}}
{{{highlight(f(x)=3(x^4-2x^3+3x^2-2x+2))}}}