Hi Sabi,
(x-2)(x²-1)>0
(x-2)(x-1)(x+1)>0
consider y=(x-2)(x-1)(x+1)
The roots will be 2,1 and -1.
3 is the highest power of x (It is degree 3)
This means that the graph will have 3 (or less, see my notes for the last question) directions.
(Since there are 3 distinct roots this one has to have 3 directions )
I do not need to do the expansion to see that the coefficient of x3 is +1.
Since it is positive, one of the ends of the graph will be in the TOP RIGHT CORNER
Always start your sketch on the right side.
Above the x axis if it is a positive leading coefficient
and below the x axis if it is a negative leading coefficient.
This is what it must look like
It can be seen from the graph that y is positive when -1<x<1 and when x>2
Any more questions the just ask :))
Hi Sabi,
(x-2)(x²-1)>0
(x-2)(x-1)(x+1)>0
consider y=(x-2)(x-1)(x+1)
The roots will be 2,1 and -1.
3 is the highest power of x (It is degree 3)
This means that the graph will have 3 (or less, see my notes for the last question) directions.
(Since there are 3 distinct roots this one has to have 3 directions )
I do not need to do the expansion to see that the coefficient of x3 is +1.
Since it is positive, one of the ends of the graph will be in the TOP RIGHT CORNER
Always start your sketch on the right side.
Above the x axis if it is a positive leading coefficient
and below the x axis if it is a negative leading coefficient.
This is what it must look like
It can be seen from the graph that y is positive when -1<x<1 and when x>2
Any more questions the just ask :))
Thanks, Melody......time constraints prevent me from explaining this in more detail......
That's ok Chris, none of us can answer all the questions in great detail. We answer what we can with as much time as we can afford to donate at that point in time.
Any correct answer is better than none, I am sure that Sabi appreciated your help :)
I like answering questions like this - it is one of my pet subject areas :))
Oh, thanks Sabi - and you are very welcome :)