• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

How many real roots does the equation . . .

This topic has 5 expert replies and 1 member reply

Top Member

How many real roots does the equation . . .

Post
How many real roots does the equation x^2y+16xy+64y=0 have if y < 0?

A. 0
B. 1
C. 2
D. 3
E. Infinite

The OA is B.

How can I determine it without knowing the value of y?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Vincen wrote:
How many real roots does the equation x^2y+16xy+64y=0 have if y < 0?

A. 0
B. 1
C. 2
D. 3
E. Infinite
Based on the answer, it looks like you're really asking us to solve for x.

Typically, the solution to an equation with 2 variables is an ordered pair of values (x,y) that satisfy the equation.
So, for example x = -8 and y = -1 is a solution to the given equation.
Likewise, x = -8 and y = -3 is a solution
...and (-8, -6) is a solution
...and (-8, -20) is a solution
Etc.

This question might be someone ambiguous to be a true GMAT question.
What's the source?

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

GMAT Instructor Default Avatar
Joined
12 Sep 2012
Posted:
2635 messages
Followed by:
117 members
Upvotes:
625
Target GMAT Score:
V51
GMAT Score:
780
Post
We could factor as follows:

x²y + 16xy + 64y = 0

y * (x² + 16x + 64) = 0

y * (x + 8)² = 0

Since y < 0, x must = -8. Since the equation is presumably a quadratic in x, we'd have one real root x. (I think the idea is that y is some known negative and that x is the only unknown, but the question is poorly phrased.)

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Post
Matt@VeritasPrep wrote:
I think the idea is that y is some known negative and that x is the only unknown, but the question is poorly phrased.)
Is x the only unknown? All we "know" about y is that it's negative.

I'm wondering if it's even okay to use the word "root" when there are 2 or more variables involved.

What do you think, Matt?

Cheers,
Brent

_________________
Brent Hanneson – Creator of GMATPrepNow.com
Use my video course along with Beat The GMAT's free 60-Day Study Guide

Sign up for free Question of the Day emails
And check out all of these free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
Post
Vincen wrote:
How many real roots does the equation x^2y+16xy+64y=0 have if y < 0?

A. 0
B. 1
C. 2
D. 3
E. Infinite
Factoring down the equation we have:

y(x^2 + 16x + 64) = 0

y(x + 8)(x + 8) = 0

y(x + 8)^2 = 0

Since y cannot be zero, x = -8, so we have 1 real root.

Answer: B

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag
Senior | Next Rank: 100 Posts Default Avatar
Joined
15 Jan 2018
Posted:
83 messages
Post
The value of y is irrelevant as it doesn't affect the rest (x^2+16x+64) which must equal zero anyway (as anything times zero must be zero).
Therefore the question can be simplified to
How many real roots does the equation x^2+16x+64=0 ?

For any quadratic equation in the form ax^2+bx+c=0, we can determine the number of roots from the
Discriminant D = b^2 - 4ac
If D < 0, there are NO real roots
If D = 0, there is 1 real root
If D >0, there are 2 real roots

From x^2+16x+64=0 , we see that a = 1, b = 16 and c = 64
Therefore D = 16^2 -4*64 = 0
Hence there is exactly 1 real root.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
Quote:
How many real roots does the equation x^2y+16xy+64y=0 have if y < 0?

A. 0
B. 1
C. 2
D. 3
E. Infinite
Hi Vincen,
Let's take a look at your question.

$$x^2y+16xy+64y=0$$
$$y\left(x^2+16x+64\right)=0$$
$$x^2+16x+64=0$$

To find the number of roots of a quadratic equation, we use the discriminant.

If Discriminant < 0, there are two distinct complex roots of the quadratic equation.
If Discriminant = 0, there is only one real root of the quadratic equation.
If Discriminant > 0, there are two distinct real roots of the quadratic equation.

So let's find the discriminant of the given equation.
$$Discriminant=b^2-4ac$$
$$=\left(16\right)^2-4\left(1\right)\left(64\right)=256-256=0$$

Since, discriminant is zero, therefore, the given equation has only one root.
Therefore, Option B is correct.

Hope it helps.
I am available if you'd like any follow up.

_________________
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

  • +1 Upvote Post
  • Quote
  • Flag
Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now.
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT

Top First Responders*

1 Scott@TargetTestPrep 40 first replies
2 Brent@GMATPrepNow 40 first replies
3 Ian Stewart 37 first replies
4 Jay@ManhattanReview 28 first replies
5 GMATGuruNY 26 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

159 posts
2 image description Max@Math Revolution

Math Revolution

84 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

59 posts
4 image description Ian Stewart

GMATiX Teacher

46 posts
5 image description GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts