What are the x-intercepts of the equation x^2 - 5x + 6 = 0?

To determine the x-intercepts of the equation (x^2 - 5x + 6 = 0), we need to find the values of (x) where the equation equals zero. These values are obtained by factoring the quadratic expression.

Start by looking for two numbers that multiply to the constant term, which is 6, and add up to the linear coefficient, which is -5. The numbers that satisfy these conditions are -2 and -3 because:

[ -2 \times -3 = 6 ] [ -2 + (-3) = -5 ]

Therefore, we can factor the quadratic equation as follows:

[ (x - 2)(x - 3) = 0 ]

Setting each factor equal to zero gives us the solutions:

[ x - 2 = 0 \quad \text{or} \quad x - 3 = 0 ]

Solving these equations leads to:

[ x = 2 \quad \text{and} \quad x = 3 ]

As such, the x-intercepts of the equation (x^2 - 5x + 6 = 0) are at