It is currently 25 Jun 2017, 00:14

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

If the equation x^3 - ax^2 +bx -a = 0 has three real roots

Author Message
TAGS:

Hide Tags

Manager
Joined: 09 Jun 2009
Posts: 210
If the equation x^3 - ax^2 +bx -a = 0 has three real roots [#permalink]

Show Tags

08 Nov 2009, 14:02
15
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

45% (02:35) correct 55% (01:40) wrong based on 216 sessions

HideShow timer Statistics

If the equation x^3 - ax^2 +bx -a = 0 has three real roots then the following id true

A. a=11
B. a not equal to 1
C. b = 1
D. b not equal to 1

How to solve equations with power 3?
Any specific tips to handle questions with such equations?
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39662

Show Tags

08 Nov 2009, 16:05
7
KUDOS
Expert's post
5
This post was
BOOKMARKED
papillon86 wrote:
If the equation x^3 - ax^2 +bx -a = 0 has three real roots then the following id true

a) a=11
b) a not equal to 1
c) b = 1
d) b not equal to 1

How to solve equations with power 3?
Any specific tips to handle questions with such equations?

I don't think we need to know how to solve cubic equation for GMAT.

For above question:

$$x^3 - ax^2 +bx -a = 0$$

$$x^2*(x-a)+(bx-a)=0$$

We are told that this equation has THREE roots. If look closer we notice that when $$b=1$$ we can write the equation as:

$$x^2*(x-a)+(x-a)=0$$ --> $$(x^2+1)*(x-a)=0$$ and this equation has only ONE root $$x=a$$.

Hence given equation to have three roots b must not equal to 1.

_________________
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1326

Show Tags

11 May 2011, 23:23
assuming b= 1

x^2(x-a)+ 1(x-a) = (x^2+1) * (x-a)

x^2 != -1 meaning b != 1.

Hence D.
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Manager
Joined: 09 Apr 2013
Posts: 148
Location: India
WE: Supply Chain Management (Consulting)
Re: If the equation x^3 - ax^2 +bx -a = 0 has three real roots [#permalink]

Show Tags

27 Nov 2013, 01:50
Good question.

The point here is to reduce the equation to x2(x-a)+bx-a=0.

Now if b=1, the equation becomes (x2+1)(x-a) = 0

The above equation has one real and two imaginary roots and hence does not satisfy the condition given in the quesiton(3 real roots)

Therefore b cannot be equal to 1.

Thanks.
_________________

+1 KUDOS is the best way to say thanks

"Pay attention to every detail"

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15961
Re: If the equation x^3 - ax^2 +bx -a = 0 has three real roots [#permalink]

Show Tags

19 Jun 2015, 08:08
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.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 9260
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If the equation x^3 - ax^2 +bx -a = 0 has three real roots [#permalink]

Show Tags

19 Jun 2015, 17:52
Hi All,

While this is an old series of posts, it's worth noting that this question is not written in proper GMAT 'style' and is not something that you'll be likely to see on Test Day. In the event that you did see this type of equation, the likely 'first step' would be to factor out an X (with the likely result that you would be left with a standard Quadratic of some kind). THAT type of Algebra IS tested on the GMAT, so you should be sure to put in the necessary work to build up your basic Algebra skills and pattern-matching abilities.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests

60-point improvement guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: If the equation x^3 - ax^2 +bx -a = 0 has three real roots   [#permalink] 19 Jun 2015, 17:52
Similar topics Replies Last post
Similar
Topics:
5 Which of the following equations has a root in common with x^2−6x+8=0 10 29 May 2017, 03:21
8 If 2 roots of an equation x^2-3x-3=0 are m and n, what is the value of 8 08 Nov 2016, 04:01
7 x^2 + bx + 72 = 0 has two distinct integer roots; how many values are 3 24 Aug 2016, 08:03
6 How many real roots does the equation x^2y+16xy+64y=0 have if y < 0? 6 21 Mar 2017, 02:05
2 In the equation ax^2 + bx + c = 0 a, b, and c are constants, 4 25 Jan 2016, 06:19
Display posts from previous: Sort by