The roots of x^2 - 5x + 6 are which pair of numbers?

• A. 2 and 4
• B. 1 and 6
• C. 2 and 3
• D. 3 and -2

Answer: (C)

When a quadratic is written as x^2 - 5x + 6, you’re looking for two numbers that multiply to the constant term and add to the coefficient of x (with the sign considered). Here, you want two numbers that multiply to 6 and add to 5. The numbers 2 and 3 fit perfectly: 2 × 3 = 6 and 2 + 3 = 5. Using those, the quadratic factors as (x - 2)(x - 3). The roots are the values of x that make each factor zero, so x = 2 or x = 3. This aligns with the quadratic formula result as well: x = [5 ± sqrt(25 - 24)]/2 = (5 ± 1)/2 → 3 or 2. So the pair of roots is 2 and 3.