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

It is currently 06 Feb 2016, 20:02
GMAT Club Tests

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

In the equation ax^2 + bx + c = 0 a, b, and c are constants,

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 18 Mar 2012
Posts: 48
GMAT 1: 690 Q V
GPA: 3.7
Followers: 0

Kudos [?]: 117 [0], given: 117

In the equation ax^2 + bx + c = 0 a, b, and c are constants, [#permalink] New post 05 Mar 2013, 10:32
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

82% (02:04) correct 18% (01:10) wrong based on 90 sessions
In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 8a then which of the following is c equal to?

A. a/12
B. a/8
C. 6a
D. 8a
E. 12a
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Mar 2013, 00:44, edited 1 time in total.
Renamed the topic and edited the question.
Intern
Intern
avatar
Joined: 18 Feb 2013
Posts: 32
GMAT 1: 710 Q49 V38
Followers: 0

Kudos [?]: 25 [0], given: 14

Reviews Badge
Re: In the equation ax^2 + bx + c = 0 [#permalink] New post 05 Mar 2013, 11:57
8a=b a=1 to make things simple
x^2+8x+c=0
given one of the roots are -2 we can factor and find the other root (x+2)(x+6)
c=12
c/a=12/1
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 630
Followers: 69

Kudos [?]: 874 [0], given: 135

Top 10 in overall
Re: In the equation ax^2 + bx + c = 0 [#permalink] New post 05 Mar 2013, 21:03
Expert's post
alexpavlos wrote:
In the equation \(ax^2 + bx + c = 0\) a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 8a then which of the following is c equal to?

a) a/12
b) a/8
c) 6a
d) 8a
e) 12a


The sum of the roots is = -b/a = -8a/a = -8. Let the other root be x. Thus, x-2 = -8

x = -6. Again, the product of the roots is -2*-6 = 12. Thus, c/a = 12. c = 12a.

E.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31228
Followers: 5342

Kudos [?]: 62064 [1] , given: 9427

Re: In the equation ax^2 + bx + c = 0 a, b, and c are constants, [#permalink] New post 06 Mar 2013, 01:09
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
alexpavlos wrote:
In the equation ax^2 + bx + c = 0 a, b, and c are constants, and abc # 0. If one root of the equation is -2, and b = 8a then which of the following is c equal to?

A. a/12
B. a/8
C. 6a
D. 8a
E. 12a


Viete's theorem states that for the roots \(x_1\) and \(x_2\) of a quadratic equation \(ax^2+bx+c=0\):

\(x_1+x_2=\frac{-b}{a}\) AND \(x_1*x_2=\frac{c}{a}\).


Thus according to the above \(x_1+x_2=-2+x_2=\frac{-b}{a}=\frac{-8a}{a}=-8\) --> \(x_2=-6\).

Also, \(x_1*x_2=-2*(-6)=\frac{c}{a}\) --> \(c=12a\).

Answer: E.

Similar questions testing this concept:
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

Hope it helps.
_________________

New to the Math Forum?
Please read this: 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 Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8158
Followers: 416

Kudos [?]: 111 [0], given: 0

Top 10 in overall
Re: In the equation ax^2 + bx + c = 0 a, b, and c are constants, [#permalink] New post 25 Jan 2016, 05:19
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: In the equation ax^2 + bx + c = 0 a, b, and c are constants,   [#permalink] 25 Jan 2016, 05:19
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic In the equation x^2+b·x+c=0, b and c are constants, and x is a variabl vinoo7 2 24 Jan 2016, 07:09
2 A quadratic equation ax^2 + bx + c = 0 has two integral roots x1 and x Learning4mU 1 10 Jan 2016, 06:55
4 Experts publish their posts in the topic Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c = Bunuel 3 06 Nov 2014, 08:23
28 Experts publish their posts in the topic If the parabola represented by f(x) = ax^2 + bx + c passes apoorvasrivastva 10 02 Mar 2010, 07:10
20 Experts publish their posts in the topic If the equation x^3 - ax^2 +bx -a = 0 has three real roots papillon86 5 08 Nov 2009, 13:02
Display posts from previous: Sort by

In the equation ax^2 + bx + c = 0 a, b, and c are constants,

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| 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®.