Final answer:
To find the solution set of the quadratic inequality x²+x-2≥0, factor the quadratic equation and examine the sign of the expression (x+2)(x-1). The solution set is x.
Step-by-step explanation:
To find the solution set of the quadratic inequality x²+x-2≥0, we can first factor the quadratic equation. Factoring x²+x-2 gives us (x+2)(x-1). The inequality becomes (x+2)(x-1)≥0. Now we can determine the values of x that satisfy the inequality by examining the sign of the expression (x+2)(x-1).
If (x+2)(x-1)≥0, then either both factors are positive or both factors are negative. This occurs when x≤-2 or x≥1, since for x≤-2, both factors are negative, and for x≥1, both factors are positive.
Therefore, the solution set of the quadratic inequality x²+x-2≥0 is x≤-2 or x≥1, which corresponds to answer choice a.