Question 927960
using roots, we have

{{{f(x)=(x-x[1])(x-x[2])}}}

1. 

if {{{x[1]=5+ 3sqrt(2)}}} and {{{x[2]=5-3sqrt(2)}}},then we have

{{{f(x)=(x-x[1])(x-x[2])}}}

{{{f(x)=(x-(5+ 3sqrt(2)))(x-(5-3sqrt(2)))}}}

{{{f(x)=(x-5-3sqrt(2))(x-5+3sqrt(2))}}}


{{{f(x)=x^2-5x+cross(3x*sqrt(2))-5x+25-15sqrt(2)-cross(3sqrt(2)*x)-15sqrt(2)+9(sqrt(2))^2}}}

{{{f(x)=x^2-5x-5x+25+cross(15sqrt(2))-cross(15sqrt(2))-9(sqrt(2))^2}}}


{{{f(x)=x^2-10x+25-18}}}


{{{f(x)=x^2-10x+7}}}


{{{ graph( 600, 600, -10, 10, -10, 10, x^2-10x+7) }}}

2. 

{{{x[1]=6+2i}}} and {{{x[2]=6-2i}}} 


{{{f(x)=(x-x[1])(x-x[2])}}}


{{{f(x)=(x-(6+2i))(x-(6-2i))}}}

{{{f(x)=(x-6-2i)(x-6+2i)}}}

{{{f(x)=x^2-6x+2xi-6x+36-12i-2ix+12i-4(i)^2 }}}   

{{{f(x)=x^2-12x+cross(2xi)+36-cross(12i)-cross(2ix)+cross(12i)-4(i)^2 }}}

{{{f(x)=x^2-12x+36-4(-1) }}}

{{{f(x)=x^2-12x+36+4 }}}

{{{f(x)=x^2-12x+40 }}}


{{{ graph( 600, 600, -10, 15, -10, 50, x^2-12x+40) }}}