Find all School-related info fast with the new School-Specific MBA Forum

It is currently 24 Oct 2014, 16:14

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the graph of y = x^2 + ax + b passes through the points

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 28 Jan 2013
Posts: 34
Followers: 0

Kudos [?]: 15 [0], given: 20

Re: If the graph of y = x^2 + ax + b passes through the points [#permalink] New post 21 Oct 2013, 01:21
Sam1 wrote:
This is how I am solving it. Will appreciate your help to tell me where I am going wrong.
since m and n are the two points through which the graph passes they will both satisfy the equation.
Hence
0=m^2+am+b
0=n^2+an+b
1-2
gives
0=n^2-m^2 +a (n-m)
taking n-m common
(n-m) (n+m+a)=0
hence (n-m)=0 or (n+m+a)=0
n=m; (n+m)=-a
looking at statement a
a^2-4=4b
a will be something in terms of b but we will not the exact value of a.
Please tell me where am I making a mistake



n and m are the roots of the equation, so

(n+m)=-a
and nm=b
and we need to find n-m. so just solve the equation to get (n-m) term.

(n-m)^2= (n+m)^2 - 4mn

put above values

(n-m)^2= (n+m)^2 - 4mn = a^2-4b = 4 (as per the given equation, i)

hence n-m = 2
Intern
Intern
avatar
Joined: 18 Sep 2013
Posts: 27
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: If the graph of y = x^2 + ax + b passes through the points [#permalink] New post 21 Oct 2013, 04:45
Chiranjeevee wrote:
Sam1 wrote:
This is how I am solving it. Will appreciate your help to tell me where I am going wrong.
since m and n are the two points through which the graph passes they will both satisfy the equation.
Hence
0=m^2+am+b
0=n^2+an+b
1-2
gives
0=n^2-m^2 +a (n-m)
taking n-m common
(n-m) (n+m+a)=0
hence (n-m)=0 or (n+m+a)=0
n=m; (n+m)=-a
looking at statement a
a^2-4=4b
a will be something in terms of b but we will not the exact value of a.
Please tell me where am I making a mistake



n and m are the roots of the equation, so

(n+m)=-a
and nm=b
and we need to find n-m. so just solve the equation to get (n-m) term.

(n-m)^2= (n+m)^2 - 4mn

put above values

(n-m)^2= (n+m)^2 - 4mn = a^2-4b = 4 (as per the given equation, i)

hence n-m = 2


Hi thank you for your reply. While I understand the part with the sum of roots. I am still a little confused of how are we ignoring the b term. Are we equating (n-m)^2 to a^2?
Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2013
Posts: 284
Followers: 0

Kudos [?]: 17 [0], given: 23

Re: If the graph of y = x^2 + ax + b passes through the points [#permalink] New post 18 May 2014, 11:19
Bunuel wrote:
gabrieldoria wrote:
Sorry I´ve got one last question after reading the whole thread.

Wouldn´t option 1 be insufficient too, because the SQ ROOT of 4 be +- 2? That would give two possible values for n-m.


No, \sqrt{4}=2, not +2 or -2.

When the GMAT provides the square root sign for an even root, such as \sqrt{x} or \sqrt[4]{x}, then the only accepted answer is the positive root. That is, \sqrt{25}=5, NOT +5 or -5.

In contrast, the equation x^2=25 has TWO solutions, +5 and -5. Even roots have only non-negative value on the GMAT.

Hope it helps.


Hi Bunuel,

This is news to me. Is this valid on ALL DS and PS problems or just one subset? Does this hold true for inequalities as well?

Also, can you suggest similar quadratics that use vieta's theorem and require us to relate roots to quadratics?

Thanks!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28917 [0], given: 2871

Re: If the graph of y = x^2 + ax + b passes through the points [#permalink] New post 19 May 2014, 02:12
Expert's post
russ9 wrote:
Bunuel wrote:
gabrieldoria wrote:
Sorry I´ve got one last question after reading the whole thread.

Wouldn´t option 1 be insufficient too, because the SQ ROOT of 4 be +- 2? That would give two possible values for n-m.


No, \sqrt{4}=2, not +2 or -2.

When the GMAT provides the square root sign for an even root, such as \sqrt{x} or \sqrt[4]{x}, then the only accepted answer is the positive root. That is, \sqrt{25}=5, NOT +5 or -5.

In contrast, the equation x^2=25 has TWO solutions, +5 and -5. Even roots have only non-negative value on the GMAT.

Hope it helps.


Hi Bunuel,

This is news to me. Is this valid on ALL DS and PS problems or just one subset? Does this hold true for inequalities as well?

Also, can you suggest similar quadratics that use vieta's theorem and require us to relate roots to quadratics?

Thanks!


Yes, this is true for all GMAT questions.

Questions involving Viete's theorem to practice:
in-the-equation-x-2-bx-12-0-x-is-a-variable-and-b-is-a-109771.html
if-x-2-3-is-one-factor-of-the-equation-x-2-4-3-x-160524.html
if-x-2-12x-k-0-is-x-155465.html
in-the-equation-ax-2-bx-c-0-a-b-and-c-are-constants-148766.html
new-algebra-set-149349-80.html#p1200987
if-q-is-one-root-of-the-equation-x-2-18x-11c-0-where-141199.html
if-f-x-5x-2-and-g-x-x-2-12x-85-what-is-the-sum-of-all-85989.html
if-4-is-one-solution-of-the-equation-x2-3x-k-10-where-139119.html
john-and-jane-started-solving-a-quadratic-equation-john-mad-106597.html
if-r-and-s-are-the-roots-of-the-equation-x-2-bx-c-141018.html

Hope this helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 13 May 2014
Posts: 40
Concentration: General Management, Strategy
Followers: 0

Kudos [?]: 28 [0], given: 1

Re: If the graph of y = x^2 + ax + b passes through the points [#permalink] New post 19 May 2014, 02:14
Sam1 wrote:
This is how I am solving it. Will appreciate your help to tell me where I am going wrong.
since m and n are the two points through which the graph passes they will both satisfy the equation.
Hence
0=m^2+am+b
0=n^2+an+b
1-2
gives
0=n^2-m^2 +a (n-m)
taking n-m common
(n-m) (n+m+a)=0
hence (n-m)=0 or (n+m+a)=0
n=m; (n+m)=-a
looking at statement a
a^2-4=4b
a will be something in terms of b but we will not the exact value of a.
Please tell me where am I making a mistake


Hi Sam1,
Basically we need to find the value of n-m, the difference between the roots.
What you have done is, showed the sum of the roots , n+m = - a ---(1) which you have deduced right.
NOW,
multiplying the above equation by n yields:
n^2+m*n = -a*n
or n^2 +m*n + a*n =0
or m*n - b = 0 ---- (as n^2+a*n+b =0 ,n being one of the roots)
or m*n = b ----------(2)

Now, (n-m)^2 = n^2 -2*m*n + m^2
= (n+m)^2 - 4*m*n

using eqn(1) and eqn(2), we have
(n-m)^2 = a^2 - 4*b
or (n-m) = sq.root(a^2 - 4*b)

Now from answer choices,using option 1,we can find n-m = 2
however,using option 2, we can not find out n-m.
Hence, A. Hope this helps.

Press kudos if you wish to appreciate
Manager
Manager
avatar
Joined: 04 Jan 2014
Posts: 128
Followers: 1

Kudos [?]: 5 [0], given: 24

Re: If the graph of y = x^2 + ax + b passes through the points [#permalink] New post 17 Jun 2014, 20:53
mbaiseasy wrote:
Given F(x) = Ax^2 + Bx + C
We could get the difference of roots with a formula:
x1-x2=\sqrt{{\frac{b^2-4ac}{a^2}}} with x1>x2



Should the denominator be a^2 or 2a?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23409
Followers: 3613

Kudos [?]: 28917 [1] , given: 2871

Re: If the graph of y = x^2 + ax + b passes through the points [#permalink] New post 18 Jun 2014, 00:32
1
This post received
KUDOS
Expert's post
pretzel wrote:
mbaiseasy wrote:
Given F(x) = Ax^2 + Bx + C
We could get the difference of roots with a formula:
x1-x2=\sqrt{{\frac{b^2-4ac}{a^2}}} with x1>x2



Should the denominator be a^2 or 2a?


It's correct as it is:

x_1=\frac{-b+\sqrt{b^2-4ac}}{2a};

x_2=\frac{-b-\sqrt{b^2-4ac}}{2a};

x_1-x_2=\frac{-b+\sqrt{b^2-4ac}}{2a}-\frac{-b-\sqrt{b^2-4ac}}{2a}=\frac{\sqrt{b^2-4ac}}{a}=\frac{\sqrt{b^2-4ac}}{\sqrt{a^2}}.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
User avatar
Joined: 31 May 2013
Posts: 12
Followers: 0

Kudos [?]: 0 [0], given: 25

GMAT ToolKit User Reviews Badge
Re: If the graph of y = x^2 + ax + b passes through the points [#permalink] New post 20 Oct 2014, 05:18
From 1, obtain 2 quadratic equations for y=x^2 + ax +b by substituting (m,0) and (n,0)

m^2 + am + b = 0
n^2 + am + b = 0

which gives

n = (-a+\sqrt{a^2-4b})/2a ; (-b-\sqrt{a^2-4b})/2a
m = (-a+\sqrt{a^2-4b})/2a ; (-b-\sqrt{a^2-4b})/2a

since n - m > 0,

n-m = \sqrt{a^2-4b}

substitute from (1) a^2-4b = 4

n-m = \sqrt{4}
n-m =2
Sufficient
Re: If the graph of y = x^2 + ax + b passes through the points   [#permalink] 20 Oct 2014, 05:18
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic M24-12-Do graphs y=ax2+b a imhimanshu 1 14 May 2013, 21:22
4 Straight line passes through the points (a,b) and (c,d). Is CasperMonday 5 28 Aug 2009, 05:17
Do lines y = A*(x^2) + b and y = C*(x^2) + d cross? 1. a = bmwhype2 2 01 Nov 2007, 06:13
2 Do lines y = a*x^2 + b and y = c*x^2 + d cross each other ? kamal.gelya 15 23 May 2007, 17:25
Line A and B pass through the point (16/5,12/5). What is the getzgetzu 1 05 May 2006, 23:27
Display posts from previous: Sort by

If the graph of y = x^2 + ax + b passes through the points

  Question banks Downloads My Bookmarks Reviews Important topics  

Go to page   Previous    1   2   [ 28 posts ] 



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

Powered by phpBB © phpBB Group and phpBB SEO

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®.