What are the zeros/roots of f(x)=x^2-2x-1

Question

Find the zeros/roots

Answer 1

f(x) = x² - 2x - 1               use completion of the square

f(x) = x² - 2x           -1

f(x) = x² -2x + 1     -1  -1

f(x) = (x - 1)² - 2

0 = (x - 1)² - 2

2 = (x - 1)²

±√2 = x - 1

1 ±√2 = x

 

{1 ± √2}