Question 852907
{{{x^2-4x+2=0}}}
{{{alpha=(4-sqrt(16-4(2)))/2=(4-sqrt(8))/2=(4-2sqrt(2))/2=2-sqrt(2)}}}
{{{beta=2+sqrt(2)}}}


{{{alpha-2=2-sqrt(2)-2=-sqrt(2)}}} and {{{beta-2=2+sqrt(2)-2=sqrt(2)}}}


The requested quadratic equation with roots {{{alpha-2}}} and {{{beta-2}}} will be {{{(x-(-sqrt(2)))(x-sqrt(2))=0}}}
{{{highlight((x+sqrt(2))(x-sqrt(2))=0)}}}
OR More Compactly,
{{{highlight(x^2-2=0)}}}