Solve the inequality x^2 - 5x + 6 ≥ 0.

• A. x < 2
• B. 2 < x < 3
• C. x ≥ 0
• D. x ≤ 2 or x ≥ 3

Answer: (D)

To find where this quadratic is nonnegative, look for where x^2 - 5x + 6 is zero or positive. Factor it as (x - 2)(x - 3). The zeros are at x = 2 and x = 3, and the parabola opens upward because the x^2 coefficient is positive.

The product (x - 2)(x - 3) is nonnegative when the two factors have the same sign. That happens for x ≤ 2 (both factors are negative) or x ≥ 3 (both factors are positive). Between 2 and 3, one factor is negative and the other positive, making the product negative, so those x don’t satisfy the inequality. Since the endpoints give zero, they are included.

Therefore, the solution set is x ≤ 2 or x ≥ 3.