Given Equation:
x² - 5x + 6 = 0

Finding Roots:
The roots of the equation x² - 5x + 6 = 0 can be found by factorizing the equation or using the quadratic formula. The factors of 6 that add up to -5 are -2 and -3. Therefore, the roots of the equation are x = 2 and x = 3.

Defining α and β:
Let α and β be the roots of the equation x² - 5x + 6 = 0. Therefore, α = 2 and β = 3.

Finding α - β:
To find the value of α - β, we simply subtract the values of α and β.
α - β = 2 - 3 = -1
Therefore, the value of α - β is -1.

Explanation:
- The given equation is a quadratic equation in the form of ax² + bx + c = 0.
- The roots of the equation are the values of x for which the equation equals zero.
- By comparing the given equation with the standard form ax² + bx + c = 0, we can determine the values of α and β.
- Once we have the values of α and β, finding α - β is a simple subtraction operation.
- In this case, the value of α - β is -1.
By following these steps, we can efficiently find the value of α - β for the given quadratic equation.