Concept: The question tests on your ability to quickly and accurately eliminate the incorrect options.
option (b) and option(c) are expanded versions of (x-1)^2 and (x+1)^2 respectively.
Their roots would be 1,1 and -1,-1 respectively and not 1 + √2 .You can eliminate them.
Now plug in 1 + √2 in the remaining options. If you observe closely, you do not need to solve.
To have a 0 of the RHS, you need to eliminate the + √2 that would be present from the x^2 terms.
This is possible in option (d) because it has a -2x . -2x would generate a -2√2 term when -2 is multiplied with 1 + √2 .