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Comment on Quadratic Inequalities
@ 4:13 you have the answer as
The expression is x² - 2x - 3
The expression is x² - 2x - 3
When x = -2, we get: x² - 2x - 3 = (-2)² - 2(-2) - 3
= (-2)(-2) - 2(-2) - 3
= 4 - (-4) - 3
= 8 - 3
= 5
Does that help?
Cheers,
Brent
I see what I did: 4 + -4
Thank you
How often does this show up
I wouldn't worry about this
I wouldn't worry about this topic. Although this question type meets the topics covered in the GRE syllabus, I have yet to see an official practice question tests it.
https://gre.myprepclub.com/forum
Hi Brent,
In the solution u provided above,
" Divide both sides by 2: x^2 > 17
This tells us that EITHER x > root17 OR x < −root17 "
Why is x < -root17 ?
I understand x > +-(root17) so, x > root 17, but why is x < - root(17) but not x > -root17
Thanks
Question link: https:/
Question link: https://gre.myprepclub.com/forum/2x-2-6-40-which-values-of-x-satisfy-the...
Let's start by examining some possible solutions to a similar inequality: x² > 16
Notice that any value of x greater than 4 will satisfy x² > 16
For example, if x = 5, we can see that 5² > 16
And, if x = 4.01, we can see that (4.01)² > 16
And, if x = 7, we can see that 7² > 16 and so on.
Now let's examine some possible NEGATIVE values of x.
For example, if x = -5, we can see that (-5)² > 16,
And, if x = -4.1, we can see that (-4.01)² > 16
And, if x = -7, we can see that (-7)² > 16 and so on.
At this point we can conclude that any values of x that's less than -4 will also satisfy the inequality.
So, if x² > 16, we know that EITHER x > 4 OR x < -4
In other words, if x² > 16, we know that EITHER x > √16 OR x < -√16
Likewise, if x² > 17, we we know that EITHER x > √17 OR x < -√17
Does that help?