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

A on edge

Step-by-step explanation:

The solution set is { x | x -2 or x 1}

Step-by-step explanation:

The given inequality is

Let us factor

so we have

Let us find zeros of

  or  

or

so we have intervals (-∞ , -2) , (-2 , 1) and (1, ∞)

we need to find in which interval is is greater than 0

so we will assume the value of x in each interval and will plug it in and will check if we get negative or positive value

Let us check the sign of in (-∞ , -2)

we can take x=-3 and plug it in

so we have

  ( which is greater than 0)

This shows  (-∞, -2) is one of the solution set

similarly we can check the sign of in (-2,1)

we take x= 0 , so we have

 ( which is less than 0)

This shows  (-2,1) is not the solution set

now we check the sign of in (1 ,∞)

we can assume x= 2, so we have

 ( which is greater than 0)

This shows  (1 ,∞) is the solution set

Hence the solution set in interval notation  (∞ ,-2)∪(1,∞)

we can write this as { x | x -2 or x 1}

bdhfnfhjffjkfjfjfjjf