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

It is currently 22 Oct 2018, 11:59

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

Looking Answer of a Quadratic Equation Question

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Intern
Intern
avatar
Joined: 12 Mar 2018
Posts: 4
Looking Answer of a Quadratic Equation Question  [#permalink]

Show Tags

New post 12 Mar 2018, 05:51
1
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

What is the largest integral value of 'k' for which the quadratic equation x2 - 6x + k = 0 will have two real and distinct roots?

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Director
Director
avatar
V
Joined: 30 Jan 2016
Posts: 756
Location: United States (MA)
Reviews Badge CAT Tests
Looking Answer of a Quadratic Equation Question  [#permalink]

Show Tags

New post Updated on: 13 Mar 2018, 16:32
1
Using discriminant:

\(x1,2=\frac{6+\sqrt{36-4k}}{2}\)=\(\frac{6+\sqrt{4*(9-k)}}{2}\)=\(\frac{6+2\sqrt{(9-k)}}{2}\)=\({3+\sqrt{(9-k)}}\). So, for the expression to have distinct real roots, \(\sqrt{9-k}\) has to be an integer, therefore k can:

k=5, x1=\({3+\sqrt{(9-5)}}=3+2=5\), or x2=\({3+\sqrt{(9-5)}}=3-2=1\)
k=8, x1=\({3+\sqrt{(9-8)}}=3+1=4\), or x2=\({3+\sqrt{(9-5)}}=3-1=2\)
k=9, x=\({3+\sqrt{(9-9)}}=3\)

So, the expression becomes \(x^2-6x+9=(x-3)^2=0\)
Attachments

diskriminant.png
diskriminant.png [ 2.58 KiB | Viewed 200 times ]


_________________

Non progredi est regredi


Originally posted by Akela on 12 Mar 2018, 11:48.
Last edited by Akela on 13 Mar 2018, 16:32, edited 7 times in total.
Director
Director
avatar
V
Joined: 30 Jan 2016
Posts: 756
Location: United States (MA)
Reviews Badge CAT Tests
Looking Answer of a Quadratic Equation Question  [#permalink]

Show Tags

New post 13 Mar 2018, 14:51
I've made a mistake in my previous post. The answer is 9 using Vieta's formula:

\(x^2-6x+k=0\)
x1+x2=6
x1*x2=k


x1 and x2 must be > 0 to maximize k and x1 and x2 cannot have different signs:

x1=1, x2=5 => x1*x2=k=5
x1=2, x2=4 => x1*x2=k=8
x1=3, x2=3 => x1*x2=k=9
_________________

Non progredi est regredi

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50042
Re: Looking Answer of a Quadratic Equation Question  [#permalink]

Show Tags

New post 17 Mar 2018, 08:20
nshtkum wrote:
What is the largest integral value of 'k' for which the quadratic equation x2 - 6x + k = 0 will have two real and distinct roots?


Please read carefully and follow our RULES OF POSTING. Thank you.

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.


If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

GMAT Club Bot
Re: Looking Answer of a Quadratic Equation Question &nbs [#permalink] 17 Mar 2018, 08:20
Display posts from previous: Sort by

Looking Answer of a Quadratic Equation Question

  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®.