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

It is currently 24 May 2019, 08:10

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 b and c are constants for which the quadratic equation x^2+bx+c=0

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

Hide Tags

 
Intern
Intern
avatar
Joined: 17 Jan 2016
Posts: 10
If b and c are constants for which the quadratic equation x^2+bx+c=0  [#permalink]

Show Tags

New post 05 May 2016, 08:41
5
39
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

59% (01:01) correct 41% (01:28) wrong based on 568 sessions

HideShow timer Statistics

If b and c are constants for which the quadratic equation \(x^2+bx+c=0\) has two different roots, what is the product of the two roots?

(1) One of the roots is 3.

(2) c = 6
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7686
Re: If b and c are constants for which the quadratic equation x^2+bx+c=0  [#permalink]

Show Tags

New post 05 May 2016, 08:44
8
11
broilerc wrote:
If b and c are constants for which the quadratic equation \(x^2+bx+c=0\) has two different roots, what is the product of the two roots?

(1) One of the roots is 3.

(2) c=6


--

Can someone elaborate please?



Hi
for a quadratic equation \(ax^2+bx+c=0\)..
SUM of roots = \(-\frac{b}{a}\)and PRODUCT of roots =\(\frac{c}{a}\)..
here a is 1, so we just require 'c'..

statement II gives us value of 'c'..
hence suff
B
_________________
General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55271
Re: If b and c are constants for which the quadratic equation x^2+bx+c=0  [#permalink]

Show Tags

New post 05 May 2016, 08:46
7
9
broilerc wrote:
If b and c are constants for which the quadratic equation \(x^2+bx+c=0\) has two different roots, what is the product of the two roots?

(1) One of the roots is 3.

(2) c=6


--

Can someone elaborate please?


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 for x^2+bx+c=0 the product of the roots will be c/1 = c.

Answer: B.
_________________
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6229
Location: United States (CA)
Re: If b and c are constants for which the quadratic equation x^2+bx+c=0  [#permalink]

Show Tags

New post 03 Aug 2016, 10:00
3
Quote:
If b and c are constants for which the quadratic equation \(x^2+bx+c=0\) has two different roots, what is the product of the two roots?

(1) One of the roots is 3.

(2) c=6


We are given that the quadratic equation x^2 + bx + c = 0 has two different roots. We need to determine the product of these two roots.

Recall that in a quadratic equation in the form ax^2 + bx + c = 0, the sum of the two roots is –b/a and the product of the two roots is c/a. Here, we are given the equation in the form of x^2 + bx + c = 0, and since a = 1, the product of the two roots is c/1 = c.

Thus, if we know the value of c, then we know the product of the two roots.

Statement One Alone:

One of the roots is 3.

We are given that one of the roots is 3. However, since we don’t know the value of the other root, we can’t determine the product of the two roots. Statement one alone is not sufficient. Eliminate choices A and D.

Statement Two Alone:

c = 6

Since we know the value of c, the product of the two roots must be 6 (see problem stem analysis above). Statement two alone is sufficient.

Answer: B
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Current Student
User avatar
Joined: 18 Oct 2014
Posts: 834
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT ToolKit User
Re: If b and c are constants for which the quadratic equation x^2+bx+c=0  [#permalink]

Show Tags

New post 03 Aug 2016, 11:15
2
broilerc wrote:
If b and c are constants for which the quadratic equation \(x^2+bx+c=0\) has two different roots, what is the product of the two roots?

(1) One of the roots is 3.

(2) c=6


--

Can someone elaborate please?


When we factorize a quadratic equation, we factorize such that sum of two roots = b and product of two roots = c*a

Here because a=1, the product will depend on the c

B is the answer
_________________
I welcome critical analysis of my post!! That will help me reach 700+
Manager
Manager
User avatar
Joined: 10 May 2014
Posts: 138
Re: If b and c are constants for which the quadratic equation x^2+bx+c=0  [#permalink]

Show Tags

New post 23 Oct 2016, 15:48
Could someone please tell me if my approach is correct?


If \(x^2 + bx +c = 0\)
Then, (x + p)(x + q) = 0

Therefore
pq = c
p + q = b

The roots of the quadratic equation will be -p and -q.
The question is asking about the product of the roots, meaning (-p)(-q) = ?
This is equal to c = ?, which in turn is equal to pq = ?

- Statement 1: Insufficient, since it only provides -p = 3 or -q = 3
- Statement 2: Sufficient.

OA = B
_________________
Consider giving me Kudos if I helped, but don´t take them away if I didn´t! :)

What would you do if you weren´t afraid?
Manager
Manager
avatar
S
Joined: 13 Dec 2013
Posts: 151
Location: United States (NY)
Concentration: General Management, International Business
Schools: Cambridge"19 (A)
GMAT 1: 710 Q46 V41
GMAT 2: 720 Q48 V40
GPA: 4
WE: Consulting (Consulting)
Reviews Badge
Re: If b and c are constants for which the quadratic equation x^2+bx+c=0  [#permalink]

Show Tags

New post 07 Apr 2017, 22:07
Bunuel wrote:
broilerc wrote:
If b and c are constants for which the quadratic equation \(x^2+bx+c=0\) has two different roots, what is the product of the two roots?

(1) One of the roots is 3.

(2) c=6


--

Can someone elaborate please?


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 for x^2+bx+c=0 the product of the roots will be c/1 = c.

Answer: B.


Hi Bunuel, is Viete's theorem needed for the GMAT? For this question can we not just deduce the answer?

1) If one root is 3, the other root could be anything. Not suff.

2) For positive c, both roots are either -ve or +ve and multiplied will give c.
In addition, for a negative c, one root will be +ve and one will be -ve. Again, multiplied together they will give c.

Suff. B
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: If b and c are constants for which the quadratic equation x^2+bx+c=0  [#permalink]

Show Tags

New post 31 Oct 2017, 12:38
For a quadratic equation, \(ax^2+bx+c=0\)
If we have two roots x1 and x2,
x1+x2 = \(-\frac{b}{a}\) and x1*x2 = \(\frac{c}{a}\)

We have been asked to find the value of x1*x2.
Given data: quadratic equation in hand that a=1

Coming to the statements :
1) One of the roots is 3.
Knowing one of the roots is not going to be enough, as the other root
can be any number and therefore, the product of the roots will be
different for every different value of the second root(Insufficient)
2) c=6
If a=1, the product of the roots is also c which is 6(Sufficient)(Option B)

_________________
You've got what it takes, but it will take everything you've got
Manager
Manager
avatar
S
Joined: 23 Sep 2016
Posts: 222
Reviews Badge
Re: If b and c are constants for which the quadratic equation x^2+bx+c=0  [#permalink]

Show Tags

New post 26 Feb 2018, 00:43
broilerc wrote:
If b and c are constants for which the quadratic equation \(x^2+bx+c=0\) has two different roots, what is the product of the two roots?

(1) One of the roots is 3.

(2) c = 6

B is the answer as product of root is c/a and statement 2 provide us enough information whereas statement A is providing only one root which is insufficient.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11010
Re: If b and c are constants for which the quadratic equation x^2+bx+c=0  [#permalink]

Show Tags

New post 01 Mar 2019, 20:05
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 Club Bot
Re: If b and c are constants for which the quadratic equation x^2+bx+c=0   [#permalink] 01 Mar 2019, 20:05
Display posts from previous: Sort by

If b and c are constants for which the quadratic equation x^2+bx+c=0

  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®.