Find the roots of the quadratic equation x^2 - 5x + 6 = 0.

The roots of x^2 - 5x + 6 = 0 are x = 2 and x = 3.

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 = 1, b = -5, and c = 6. Substituting these values into the quadratic formula, we get:

x = (-(-5) ± √((-5)^2 - 4(1)(6))) / 2(1)
x = (5 ± √(25 - 24)) / 2
x = (5 ± 1) / 2

So the roots of the equation are x = 2 and x = 3. We can check this by substituting these values back into the original equation:

2^2 - 5(2) + 6 = 0
3^2 - 5(3) + 6 = 0

Both of these equations are true, so we have found the correct roots.