Final answer:
The solution set of the inequality x^2 + x - 2 ≥ 0 is found by factoring the quadratic expression, identifying the critical points, testing values from each interval, and determining the intervals where the inequality holds true, which are x ≤ -2 and x ≥ 1.
Step-by-step explanation:
The solution set of the quadratic inequality x^2 + x - 2 ≥ 0 can be found by first factoring the quadratic expression on the left side. The expression factors into (x + 2)(x - 1). We set each factor equal to zero to find the critical points. Therefore, x + 2 = 0 yields x = -2, and x - 1 = 0 yields x = 1. These are the points where the inequality will change its sign.
To determine the intervals where the inequality holds true (is non-negative), we test values from the intervals x < -2, -2 < x < 1, and x > 1. By testing these intervals in the inequality, it is determined that the solution set includes the intervals x ≤ -2 and x ≥ 1. Hence, the correct option is A. x .