Find the roots of the quadratic equation 3x^2 - 4x + 1 = 0.

The roots of the quadratic equation 3x^2 - 4x + 1 = 0 are 1/3 and 1.

To find the roots of a quadratic equation in the form ax^2 + bx + c = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. In this case, a = 3, b = -4, and c = 1, so we have:

x = (-(-4) ± √((-4)^2 - 4(3)(1))) / (2(3))
x = (4 ± √(16 - 12)) / 6
x = (4 ± √4) / 6
x = (4 ± 2) / 6

So the roots are x = (4 + 2) / 6 = 1/3 and x = (4 - 2) / 6 = 1. We can check these roots by plugging them back into the original equation:

3(1/3)^2 - 4(1/3) + 1 = 0
1 - 4/3 + 1 = 0
2/3 = 2/3

3(1)^2 - 4(1) + 1 = 0
3 - 4 + 1 = 0
0 = 0

Both roots satisfy the equation, so we can be confident that our answer is correct.