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What is the solution set of the quadratic inequality x^2 + x - 2 ≥ 0?

A. x ≤ -2 or x ≥ 1
B. x
C. x^2 - 2 or x ≤ 1
D. x^2 - 1 or x ≤ 2

1 Answer

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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 .

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