Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 25 May 2017, 00:19

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Solving Quadratic Inequalities: Graphic Approach

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 38859
Followers: 7728

Kudos [?]: 106067 [4] , given: 11607

### Show Tags

23 Apr 2014, 11:57
4
KUDOS
Expert's post
37
This post was
BOOKMARKED

Say we need to find the ranges of $$x$$ for $$x^2-4x+3<0$$. $$x^2-4x+3=0$$ is the graph of a parabola and it look likes this:

Intersection points are the roots of the equation $$x^2-4x+3=0$$, which are $$x_1=1$$ and $$x_2=3$$. "<" sign means in which range of $$x$$ the graph is below x-axis. Answer is $$1<x<3$$ (between the roots).

If the sign were ">": $$x^2-4x+3>0$$. First find the roots ($$x_1=1$$ and $$x_2=3$$). ">" sign means in which range of $$x$$ the graph is above x-axis. Answer is $$x<1$$ and $$x>3$$ (to the left of the smaller root and to the right of the bigger root).

This approach works for any quadratic inequality. For example: $$-x^2-x+12>0$$, first rewrite this as $$x^2+x-12<0$$ (so that the coefficient of x^2 to be positive. It's possible to solve without rewriting, but easier to master one specific pattern).

$$x^2+x-12<0$$. Roots are $$x_1=-4$$ and $$x_1=3$$ --> below ("<") the x-axis is the range for $$-4<x<3$$ (between the roots).

Again if it were $$x^2+x-12>0$$, then the answer would be $$x<-4$$ and $$x>3$$ (to the left of the smaller root and to the right of the bigger root).

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 38859
Followers: 7728

Kudos [?]: 106067 [0], given: 11607

### Show Tags

28 May 2014, 04:23
Expert's post
3
This post was
BOOKMARKED
Check out all important topics we have in Main Math forum HERE.

Important topics in PS forums.

Important topics in DS forums.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15434
Followers: 649

Kudos [?]: 207 [0], given: 0

### Show Tags

12 Jul 2015, 11:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15434
Followers: 649

Kudos [?]: 207 [0], given: 0

### Show Tags

17 Jul 2016, 22:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Similar topics Replies Last post
Similar
Topics:
12 Inequalities - Quadratic Inequalities 3 13 May 2017, 11:33
3 Articles for solving quadratic equations using graphical approach 1 15 Sep 2016, 20:14
2 inequality graphical approach, what to shade? see inside ... 2 25 Sep 2013, 07:34
Solving Inequalities Graphically: Is Graph Paper Allowed 7 25 Jan 2010, 23:37
177 Graphic approach to problems with inequalities 115 19 May 2016, 22:06
Display posts from previous: Sort by