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The correct answer is option D.

The function has a repeated root. We can find this by factorization.

x² - 2x + 1
= x² - x - x + 1
= x (x - 1) - 1(x - 1)
= (x -1)(x - 1)

This can also be checked by finding the discriminant. The discriminant is zero which shows the function has a repeated root.