In the equation ax^2 + bx + c = 0 a, b, and c are constants, : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 17:10

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 18 Mar 2012
Posts: 48
GMAT 1: 690 Q V
GPA: 3.7
Followers: 0

Kudos [?]: 187 [0], given: 117

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

### Show Tags

05 Mar 2013, 10:32
2
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

82% (02:04) correct 18% (01:10) wrong based on 110 sessions

### HideShow timer Statistics

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
Joined: 18 Feb 2013
Posts: 32
GMAT 1: 710 Q49 V38
Followers: 0

Kudos [?]: 30 [0], given: 14

Re: In the equation ax^2 + bx + c = 0 [#permalink]

### Show Tags

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
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 80

Kudos [?]: 1116 [0], given: 136

Re: In the equation ax^2 + bx + c = 0 [#permalink]

### Show Tags

05 Mar 2013, 21:03
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7066

Kudos [?]: 92917 [1] , given: 10528

Re: In the equation ax^2 + bx + c = 0 a, b, and c are constants, [#permalink]

### Show Tags

06 Mar 2013, 01:09
1
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, $$x_1*x_2=-2*(-6)=\frac{c}{a}$$ --> $$c=12a$$.

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

Hope it helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13416
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: In the equation ax^2 + bx + c = 0 a, b, and c are constants, [#permalink]

### Show Tags

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.
_________________
Re: In the equation ax^2 + bx + c = 0 a, b, and c are constants,   [#permalink] 25 Jan 2016, 05:19
Similar topics Replies Last post
Similar
Topics:
2 If –6 and 3 are the solutions to the equation x^2 + bx + c = 0, where 3 02 Nov 2016, 01:01
5 In the equation x^2+b·x+c=0, b and c are constants, and x is a variabl 2 24 Jan 2016, 07:09
5 Let f(x) = x^2 + bx + c. If f(6) = 0 and f(-3) = 0, then b + c = 3 06 Nov 2014, 08:23
37 If the parabola represented by f(x) = ax^2 + bx + c passes 11 02 Mar 2010, 07:10
24 If the equation x^3 - ax^2 +bx -a = 0 has three real roots 5 08 Nov 2009, 13:02
Display posts from previous: Sort by