Answer
$x^2-2x-1$
Work Step by Step
Write the quadratic as the product of two linear factors and the leading coefficient: $a(x-r_1)(x-r_2)=0$, where $r_1$ and $r_2$ are the solutions.
$a[x-(1+\sqrt 2)][x-(1-\sqrt 2)]=0~~$ (Make $a=1$ since it can be any real number except $0$)
$(x-1-\sqrt 2)(x-1+\sqrt 2)=0$
$(x-1)^2-(\sqrt 2)^2=0$
$x^2-2x+1-2=0$
$x^2-2x-1$ (general form)
