Hi
When we take the inequality (x-3)*(x-6)>0, I understand that this eq is a parabola that passes through the X-axis at x=3 and x=6.
This also shows that the expression is positive between x>3 and x<6.
Now my question is:
We generally say the solution to the above inequality is 3<x<6.
So, if one sees (x-3)*(x-6) > 0, then is there a way to arrive at 3<x<6
or
Should we just think that as the roots are 3 and 6, and 3 being smaller, the equation has to be positive between 3 and 6.
Ex: if I say (x-a)*(x-b) > 0, I don't know whether the solution is a<x<b or b<x<a.
is there a way to arrive at this?
When we take the inequality (x-3)*(x-6)>0, I understand that this eq is a parabola that passes through the X-axis at x=3 and x=6.
This also shows that the expression is positive between x>3 and x<6.
Now my question is:
We generally say the solution to the above inequality is 3<x<6.
So, if one sees (x-3)*(x-6) > 0, then is there a way to arrive at 3<x<6
or
Should we just think that as the roots are 3 and 6, and 3 being smaller, the equation has to be positive between 3 and 6.
Ex: if I say (x-a)*(x-b) > 0, I don't know whether the solution is a<x<b or b<x<a.
is there a way to arrive at this?