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

It is currently 19 Sep 2018, 13:44

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

If k and -k are the solutions to x^4 - 10x^2 + 25 = 0, where k is a po

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49251
If k and -k are the solutions to x^4 - 10x^2 + 25 = 0, where k is a po  [#permalink]

Show Tags

New post 01 Feb 2017, 10:36
2
5
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

94% (01:04) correct 6% (02:04) wrong based on 150 sessions

HideShow timer Statistics

Retired Moderator
avatar
V
Joined: 28 May 2014
Posts: 528
GMAT 1: 730 Q49 V41
GMAT ToolKit User Premium Member
Re: If k and -k are the solutions to x^4 - 10x^2 + 25 = 0, where k is a po  [#permalink]

Show Tags

New post 01 Feb 2017, 21:49
1
Solutions of x^4 - 10x^2 + 25 = 0 are √k and - √k;

So we can say x = √k and x = - √k and x^2 = k;

Now,
x^4 - 10x^2 + 25 = 0
=> (x^2 -5)^2 = 0
=> x^2 -5 = 0
=> x^2 = 5
=> k = 5; Hence, ans D.


Cheers.
_________________

440 to 730: If I Can, You Can Too

CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 2854
Location: Canada
Re: If k and -k are the solutions to x^4 - 10x^2 + 25 = 0, where k is a po  [#permalink]

Show Tags

New post 02 Feb 2017, 09:14
2
Top Contributor
1
Bunuel wrote:
If \(\sqrt{k}\) and \(-\sqrt{k}\) are the solutions to x^4 - 10x^2 + 25 = 0, where k is a positive constant, then k =

A. 0
B. 1
C. 3
D. 5
E. 10


Let's first solve the equation x⁴ - 10x² + 25 = 0
Factor to get: (x² - 5)(x² - 5) = 0
So, it must be the case that x² - 5 = 0
Take x² - 5 = 0 and add 5 to both sides to get: x² = 5

So, x = √5 or x = -√5
We're told that the solutions are √k and -√k
This means that k = 5

Answer: D

Cheers,
Brent
_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2835
Re: If k and -k are the solutions to x^4 - 10x^2 + 25 = 0, where k is a po  [#permalink]

Show Tags

New post 08 Feb 2017, 11:35
Bunuel wrote:
If \(\sqrt{k}\) and \(-\sqrt{k}\) are the solutions to x^4 - 10x^2 + 25 = 0, where k is a positive constant, then k =

A. 0
B. 1
C. 3
D. 5
E. 10


Let’s start by factoring x^4 - 10x^2 + 25 = 0:

(x^2 - 5)(x^2 - 5) = 0

Thus:

x^2 - 5 = 0

x^2 = 5

x = √5 or x = -√5, and thus k = 5.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8095
Premium Member
Re: If k and -k are the solutions to x^4 - 10x^2 + 25 = 0, where k is a po  [#permalink]

Show Tags

New post 11 Jun 2018, 06:42
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If k and -k are the solutions to x^4 - 10x^2 + 25 = 0, where k is a po &nbs [#permalink] 11 Jun 2018, 06:42
Display posts from previous: Sort by

If k and -k are the solutions to x^4 - 10x^2 + 25 = 0, where k is a po

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

Events & Promotions

PREV
NEXT


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®.