Question

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

a) x ≤ -2 or x ≥ 1
b) x ≤ -1 or x ≥ 2
c) x ≤ 1 or x ≥ -2
d) x ≤ -1 and x ≥ 2

Answer 1

The solution set of the quadratic inequality x^2 + x - 2 ≥ 0 is x ≤ -2 or x ≥ 1. The correct answer is option a) x ≤ -2 or x ≥ 1

Step-by-step explanation:

To find the solution set of the quadratic inequality x^2 + x - 2 ≥ 0, we can try to factorize the expression. However, since this expression cannot be easily factorized, we can solve it using the quadratic formula.

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = -2. Plugging these values into the quadratic formula:

x = (-1 ± √(1^2 - 4(1)(-2))) / (2(1))

x = (-1 ± √(1 + 8)) / 2

x = (-1 ± √9) / 2

x = (-1 ± 3) / 2

So, the two solutions are x = (-1 + 3) / 2 = 1 and x = (-1 - 3) / 2 = -2.

The solution set of the quadratic inequality x^2 + x - 2 ≥ 0 is x ≤ -2 or x ≥ 1.