Your work is perfect right up until you determined that x^2=1
At this point, there are 2 possible solutions: x = 1 and x = -1

Cheers,
Brent

How many distinct roots does the equation x� - 2x² + 1 = 0 have?
A) 0
B) 1
C) 2
D) 3
E) 4

Here's my solution.
First notice that x� = (x²)²

Now, we'll use something called "u-substitution"

Let u = x²
So, we can take the equation replace x² with u to get: u² - 2u + 1 = 0
Factor to get: (u - 1)(u - 1) = 0
Solve, to get u = 1

Now that we know that u = 1, we'll recognize that u = x²
So, we now know that x² = 1

If x² = 1, then we have two possible solutions: x = 1 and x = -1
Since the equation has two distinct roots (solutions), the correct answer is C

Cheers,
Brent