x^2-x-2 <0

Question

What is the solution set? 

Answer 1

If our zeros are x=-1 and x=2, then we need to use test points to see which x values make the left side of the inequality negative.

 

Use test points   x=-2, x=0, and x=3.

 

(-2 - 2)(-2 + 1) = -4 / -1 = 4

 

(0 - 2)(0 + 1) = -2 / 1 = -2

 

(3 - 2)(3 + 1) = 1 / 4

 

 

x=0 makes the inequality true.  You solution set is all real numbers between -1 and 2.

Answer 2

(x-2)(x+1)<0

 

the solution is either x<2 or x<-1

 

then the solution is x=(2,-1)U(-1,∞) because if x=-1 the function will equal 0 and 0 is not less than 0