GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 12 Nov 2018, 20:53

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Essential GMAT Time-Management Hacks

     November 14, 2018

     November 14, 2018

     07:00 PM PST

     08:00 PM PST

    Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST
  • $450 Tuition Credit & Official CAT Packs FREE

     November 15, 2018

     November 15, 2018

     10:00 PM MST

     11:00 PM MST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)

If a and b are constants, and the equation [m]x^3 +ax^2 +bx = 64[/m] h

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Senior DS Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 1066
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
If a and b are constants, and the equation [m]x^3 +ax^2 +bx = 64[/m] h  [#permalink]

Show Tags

New post 27 Oct 2018, 09:27
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

54% (01:11) correct 46% (01:48) wrong based on 23 sessions

HideShow timer Statistics

If a and b are constants, and the equation \(x^3 +ax^2 +bx = 64\) has precisely one solution for x, what is the value of b?
A) 48
B) 16
C) 24
D) -16
E) -67

Weekly Quant Quiz #6 Question No 9


_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Senior DS Moderator
User avatar
D
Joined: 27 Oct 2017
Posts: 1066
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Premium Member CAT Tests
Re: If a and b are constants, and the equation [m]x^3 +ax^2 +bx = 64[/m] h  [#permalink]

Show Tags

New post 27 Oct 2018, 09:27
Because if this cubic polynomial has only one root, 4 , then the equation can be written as:

(x - 4)^3 = 0

And then when we expand this we will get :

\(x^3 - 3*4*x^2 + 3*4^2*x - 64 = 0\)

Hence comparing to equation given, we get b = 48
_________________

Win GMAT CLUB Test- Weekly Quant Quiz Contest
Weekly Quant Quiz Questions- Direct Download
SC: Confusable words

All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory
Error log/Key Concepts
Combination Concept: Division into groups
Question of the Day (QOTD)
Free GMAT CATS

Intern
Intern
avatar
B
Joined: 26 Mar 2018
Posts: 1
Re: If a and b are constants, and the equation [m]x^3 +ax^2 +bx = 64[/m] h  [#permalink]

Show Tags

New post 27 Oct 2018, 22:47
x=4. using sum of multiplication of roots b=48
Manager
Manager
avatar
G
Joined: 14 Jun 2018
Posts: 179
CAT Tests
Re: If a and b are constants, and the equation [m]x^3 +ax^2 +bx = 64[/m] h  [#permalink]

Show Tags

New post 27 Oct 2018, 23:31
\(x^3+ax^2+bx-64 = 0\)
let the root = k
product of roots = -(-64)/1 = 64
since the roots are the same , \(k^3 = 64 ; k = 4\)

sum of root = -a/1
a = -12

putting the value of x in the equation ,
64 + 16a + 4b = 64
16a+4b = 0
4a + b = 0
b = -4a = 48
Intern
Intern
avatar
B
Joined: 21 Aug 2018
Posts: 3
Re: If a and b are constants, and the equation [m]x^3 +ax^2 +bx = 64[/m] h  [#permalink]

Show Tags

New post 28 Oct 2018, 02:47
I got A for the answer.

x3+ax2+bx=64
<=> x^3 + ax^2 + bx - 64 = 0

Vieta's theorem
x1*x2*x3 = -(-64)/1

Since there is only 1 value of x (x1, x2 and x3 are the same), meaning x^3 = 64 => x=4

x1x2 +x2x3 + x3x1 = b/1
or 4*4 + 4*4 +4 *4 = 16 + 16 + 16 = 48
GMAT Club Bot
Re: If a and b are constants, and the equation [m]x^3 +ax^2 +bx = 64[/m] h &nbs [#permalink] 28 Oct 2018, 02:47
Display posts from previous: Sort by

If a and b are constants, and the equation [m]x^3 +ax^2 +bx = 64[/m] h

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.