x2-4x-12<0

Question

I am trying to solve this problem and i cant i really need help i looked it up and   this is the next step but how do you get the (x+2)(x-6)<0 how do you get the 6 in the next step 

Answer 1

Sarah, you are right in factoring the quadratic equation and set it up as (x+2)(x-6)<0

 

The next step is treat the problem as if you are solving for x in the quadratic equation when it equals to zero. The only difference is you got two sets of inequalities to solve for. However, be careful in which direction the inequality sign is. 

 

x+2<0 or x-6<0

  -2  -2      +6 +6

 

x<-2   or     x<6 To test if any of the inequalities is true, pick a value of x. Let x=0 and substitute it into the original equation. 0^2-4(0)-12=-12<0  Hence, x<6 is true.

 

Pick x=-3 and substitute it ito the original equation. (-3)^2-4(-3)-12=9+12-12=9<0 in which is not true. Thus, x>-2 is the other solution. Therefore, the overall solution that satisfy this inequality is:

 

-2<x<6