What are the roots of the equation x² - 5x + 6 = 0?

To find the roots of the quadratic equation x² - 5x + 6 = 0, we can use factoring. The goal is to express the quadratic in factored form, which takes the form (x - p)(x - q) = 0, where p and q are the roots we seek.

First, we need two numbers that multiply to the constant term, which is 6, and add up to the coefficient of the linear term, which is -5. The pair of numbers that fulfills these criteria are -2 and -3, since:

• (-2) * (-3) = 6 (they multiply to the constant term)

• (-2) + (-3) = -5 (they add up to the linear coefficient)

Thus, we can rewrite the equation as:

(x - 2)(x - 3) = 0.

Setting each factor equal to zero gives us the roots:

x - 2 = 0 → x = 2,

x - 3 = 0 → x = 3.

As a result, the roots of the equation are x = 2 and x = 3. This matches the correct choice, confirming that these values are indeed the solutions