Ontario Mathematics Proficiency Practice Test

To determine the roots of the quadratic equation \( x^2 - 5x + 6 = 0 \), we can factor the equation. The goal of factoring is to express the quadratic in a form that clearly reveals its roots, typically in the format \( (x - p)(x - q) = 0 \), where \( p \) and \( q \) are the roots.

Starting with \( x^2 - 5x + 6 \), we need to find two numbers that multiply to \( 6 \) (the constant term) and add up to \( -5 \) (the coefficient of the \( x \) term). The numbers that satisfy these conditions are \( -2 \) and \( -3 \).

Thus, we can rewrite the equation as:

\[

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

\]

From this factored form, we can see that the roots are \( x = 2 \) and \( x = 3 \). By setting each factor equal to zero, we find:

1. \( x - 2 = 0 \) leads to \( x = 2 \)

2. \( x - 3 = 0