It is currently 30 Nov 2021, 00:17 |

Customized

for You

Track

Your Progress

Practice

Pays

- Nov
**29**### MBA Spotlight Fair - Nov 29 with Top 50 MBA/MiM Programs

06:00 AM PST

-12:00 PM PST

An MBA/MiM Fair with Innovative Format is coming at the end of November, just in time for R2! Meet 50 MBA & MiM programs in only 3 days! Special Bonus: GMAT Club Tests to boost your score before R2! - Dec
**02**### Free GRE Prep Hour with Manhattan Prep

08:00 PM EST

-09:00 PM EST

Strategies and techniques for approaching featured GRE topics, 1-hour of live, online instruction - Dec
**07**### Ignite Your GRE® Quant Score

01:00 PM EST

-08:00 PM EST

Target Test Prep GRE Quant is a unique, comprehensive online course that combines innovative software with time-tested study methods to prepare you for the rigors of the GRE. Try our course for 5 days for just $1(no automatic billing) - Dec
**08**### Greenlight Test Prep - Free Content

07:00 PM PST

-08:00 PM PST

Regardless of whether you choose to study with Greenlight Test Prep, we believe you'll benefit from these free resources. Free GRE Prep Study Guide, Free Video Modules, and more

If a > 0 and b < 0, which of the following statements are t
[#permalink]
15 Jun 2017, 07:37

2

Expert Reply

Question Stats:

If a > 0 and b < 0, which of the following statements are true about the values of x that solve the equation \(x^2\) – ax + b = 0?

Indicate all such statements.

❑ They have opposite signs.

❑ Their sum is greater than zero.

❑ Their product equals –b.

_________________

GRE Prep Club OFFICIAL Android App

New to the GRE, and GRE CLUB Forum?

GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)

Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection

Books: All GRE Best Books

Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

New to the GRE, and GRE CLUB Forum?

GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ

Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)

Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests

GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection

Books: All GRE Best Books

Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)

How is the GRE Score Calculated -The Definitive Guide (2021)

Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)

Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021)

Re: If a > 0 and b < 0, which of the following statements are t
[#permalink]
24 Sep 2017, 08:41

My strategy has been to write an example of second degree equation that is easy to solve as x^2-x-4 = 0, where a = 1 and b = -4. This is easily factorized as (x-2)(x+1) = 0 so that the solutions are 2 and -1. Thus, we can screening our choices:

❑ They have opposite signs: 2 and -1 have opposite signs -> CORRECT

❑ Their sum is greater than zero: 2 + (-1) = 1 >0 -> CORRECT

❑ Their product equals –b: 2*(-1) = -2 while b = -4 -> WRONG

Answers are A and B!

❑ They have opposite signs: 2 and -1 have opposite signs -> CORRECT

❑ Their sum is greater than zero: 2 + (-1) = 1 >0 -> CORRECT

❑ Their product equals –b: 2*(-1) = -2 while b = -4 -> WRONG

Answers are A and B!

Re: If a > 0 and b < 0, which of the following statements are t
[#permalink]
21 Aug 2018, 03:09

2

for equation ax^2+bx+c = 0

sum of roots = -b/a

product of roots = c/a

In case of this question:

x^2-ax+b = 0

sum of roots = a (since a> 0 , option b is correct)

product of roots = b (option c incorrect)

product of roots = b and since b is less than 0 , therefore both roots should be of opposite sign (option a correct)

sum of roots = -b/a

product of roots = c/a

In case of this question:

x^2-ax+b = 0

sum of roots = a (since a> 0 , option b is correct)

product of roots = b (option c incorrect)

product of roots = b and since b is less than 0 , therefore both roots should be of opposite sign (option a correct)

Re: If a > 0 and b < 0, which of the following statements are t
[#permalink]
11 Dec 2019, 04:44

Any other solution?

_________________

_________________

New to the GRE, and GRE CLUB Forum?

GRE: All About GRE | Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All In One Resource's | All Quant Questions Collection | All Verbal Questions Collection | Manhattan 5lb All Questions Collection

Books: All GRE Best Books

Scores: Average GRE Score Required By Universities in the USA

Tests: All Free & Paid Practice Tests | GRE Prep Club Tests

Extra: Permutations, and Combination

Vocab: GRE Vocabulary

Facebook GRE Prep Group: Click here to join FB GRE Prep Group

GRE: All About GRE | Search GRE Specific Questions | Download Vault

Posting Rules: QUANTITATIVE | VERBAL

Questions' Banks and Collection:

ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides

3rd Party Resource's: All In One Resource's | All Quant Questions Collection | All Verbal Questions Collection | Manhattan 5lb All Questions Collection

Books: All GRE Best Books

Scores: Average GRE Score Required By Universities in the USA

Tests: All Free & Paid Practice Tests | GRE Prep Club Tests

Extra: Permutations, and Combination

Vocab: GRE Vocabulary

Facebook GRE Prep Group: Click here to join FB GRE Prep Group

Re: If a > 0 and b < 0, which of the following statements are t
[#permalink]
26 Oct 2020, 12:10

Okay so this problem is a bit tricky, I have few comments and the feedback is most appreciated.

My first notice is the importance of the conditions given, so we know the (a) > 0 , (b) < 0.

Moreover, we see in the equation given that: x^2 - ax +b = 0

Considering the first condition we see that the equation is really in this shape: x^2 - ax - b ; because b is a negative number.

If their sum in the equation is negative then after we factor them and solve they are going to change signs and thus their sum after becoming the solutions is a positive sum.

And the tricky part regarding their multiplication is irrelevant, they would never equal to -b because their multiplication is going to be definitely negative( they have opposite signs) and b < 0; so -b == +ve value.

It becomes much clearer as you demonstrate it on a simple equation as mentioned in the above comments.

My first notice is the importance of the conditions given, so we know the (a) > 0 , (b) < 0.

Moreover, we see in the equation given that: x^2 - ax +b = 0

Considering the first condition we see that the equation is really in this shape: x^2 - ax - b ; because b is a negative number.

If their sum in the equation is negative then after we factor them and solve they are going to change signs and thus their sum after becoming the solutions is a positive sum.

And the tricky part regarding their multiplication is irrelevant, they would never equal to -b because their multiplication is going to be definitely negative( they have opposite signs) and b < 0; so -b == +ve value.

It becomes much clearer as you demonstrate it on a simple equation as mentioned in the above comments.

gmatclubot

Moderators:

Multiple-choice Questions — Select One or More Answer Choices |
||