SOLUTION: Even though this has a greater than sign is it still a quadratic problem? I am stuck not sure how to solve it. x^2-6x>-8

Question 82730: Even though this has a greater than sign is it still a quadratic problem? I am stuck not sure how to solve it.
x^2-6x>-8
Answer by kev82(151) (Show Source): You can put this solution on YOUR website!
Hi,

It is still a quadrtic problem, yes. This is a quadratic inequality, I assume you are used to dealing with quadratic equations. You'll be pleased to know solving them isn't much harder.

The first thing to do is rewrite it like you would a quadratic equation:

Now, there are three situations, when it is greater than zero, when it is equal to zero, and when it is less than zero. Now because it's continuous (umm, if you don't know what that means forget I said it) then to change from greater than zero to less than zero, it must pass through zero first. So if we find out when it equals zero that tells us the interesting change points. So let's solve it for zero.

So the interesting points where it changes are at x=2 and x=4. This means that the regions of interest(regions are seperated by when it changes) are:

To find out if it is bigger than or less than zero in a region we just pick a number (any number) in the region, and subsitiute it in.

For the first region

I'll try x=-10.

. 168 is defintely bigger than 0, so here the inequality is true. Let's try region 2, I'll pick x=3.

So the inequality isn't true here. Try region 3 yourself, just pick a number that's bigger than 4, and substitute it in, and see wheteher it's smaller than or bigger than 0. You should find it's bigger.

So, the inequality holds when

and that's the answer.

Hope that helps,
Kev
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