#2**+5 **

x2 > 2(x + 4)

You can also do a question like this graphically - which is what I would normally do.

$$x^2>2x+8\\\\

x^2-2x-8>0\\\\

\mbox{You can think of it like this. }\\\\

x^2-2x-8=y \mbox{ Where y is positive}\\\\

y=(x-4)(x+2)\mbox{ Where y is positive}\\\\$$

y=0 when x-4=0 that is when x=4 and also whatn x+2=0 that is when x=-2

So the two roots are x=4 and x=-2.

This is a concave up parabola because the number in front of the x^{2} is +1 (the + indicates concave up)

Do a very quick sketch - you don't need a vertex or any other features.

I'll do a good sketch because with the computer graphing programs it is too difficult to do a rough one.

You can see from the diagram that y is postive when x>4 and when x<-2

Melody
Jun 27, 2014

#1**+5 **

Let's move everything to the left side and distribute the two

x^2 -2x-8>0

(x-4)(x+2)>0

We can see that the two zeroes are at x=4 and x=-2, neither of which are solutions! They are important because we can use them to determine what segment(s) of the number line contain our solution set. Let's try testing 3 numbers, one that is greater than our two zeroes, one that is less than our two zeroes, and one that is between our zeroes.

Greater than: I'll choose x=1000 because it will make it easy to determine if our inequality holds. Note that when you substitute a large number like this it makes both factors of our quadratic positive, which guarantees our inequality is true.

Between: I choose x=0 because it is easy to calculate. (0-4)(0+2)>0 is equivalent to -8>0 which is clearly false.

Less than: let's pick a big negative number. It really does not matter what it is but when we select any large negative number we get two negative facts which result in a positive produce which guarantees our inequality is satisfied

Therefore our solution set is x>4 or x<-2

jboy314
Jun 27, 2014

#2**+5 **

Best Answer

x2 > 2(x + 4)

You can also do a question like this graphically - which is what I would normally do.

$$x^2>2x+8\\\\

x^2-2x-8>0\\\\

\mbox{You can think of it like this. }\\\\

x^2-2x-8=y \mbox{ Where y is positive}\\\\

y=(x-4)(x+2)\mbox{ Where y is positive}\\\\$$

y=0 when x-4=0 that is when x=4 and also whatn x+2=0 that is when x=-2

So the two roots are x=4 and x=-2.

This is a concave up parabola because the number in front of the x^{2} is +1 (the + indicates concave up)

Do a very quick sketch - you don't need a vertex or any other features.

I'll do a good sketch because with the computer graphing programs it is too difficult to do a rough one.

You can see from the diagram that y is postive when x>4 and when x<-2

Melody
Jun 27, 2014