Question 1061041
Try starting with factored form of a quadratic equation.

{{{(x-p)(x-v)=0}}}
and you have {{{sqrt(2)-1}}} as one of the roots.  Maybe the other root is the conjugate of the known root?  You might expect {{{-sqrt(2)-1}}}., or  {{{-1-sqrt(2)}}}.


Let's see if working in reverse direction starting with the two roots.
{{{(x-(-1+sqrt(2)))(x-(-1-sqrt(2)))=0}}}------will this work?


{{{(x+1-sqrt(2))(x+1+sqrt(2))=0}}}

{{{((x+1)-sqrt(2))((x+1)+sqrt(2))=0}}}, and recognize that give difference of squares;

{{{(x+1)^2-(sqrt(2))^2=0}}}

{{{x^2+2x+1-2=0}}}

{{{x^2-2x-1=0}}}  in which {{{system(a=1,b=-2,c=-1)}}}.


Both the given root and its conjugate are roots for this equation.


Your text book should also give a lesson on what happens when you determine the product of roots of a quadratic equation; and what happens when you take the sum of the roots of a quadratic equation.