Which pair of numbers are the roots of the equation x^2 - 5x + 6 = 0?

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

Answer: (B)

To find the roots by factoring, look for two numbers whose product is the constant term and whose sum is the coefficient of x. For x^2 - 5x + 6, we want two numbers that multiply to +6 and add to -5. Those numbers are -2 and -3. This lets us factor the quadratic as (x - 2)(x - 3) = 0. Setting each factor to zero gives x = 2 or x = 3. You can check: 2^2 - 5·2 + 6 = 0 and 3^2 - 5·3 + 6 = 0. So the roots are 2 and 3. The other pairs don’t satisfy the equation when substituted, so they aren’t roots.