• NEW! FREE Beat The GMAT Quizzes  Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 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 PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## How many real roots does the equation . . . tagged by: Brent@GMATPrepNow ##### This topic has 5 expert replies and 1 member reply ### Top Member ## How many real roots does the equation . . . 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? ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13033 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 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 Sign up for free Question of the Day emails And check out all of these free resources 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 Joined 12 Sep 2012 Posted: 2635 messages Followed by: 117 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 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.) 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 GMAT Instructor Joined 08 Dec 2008 Posted: 13033 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 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 Sign up for free Question of the Day emails And check out all of these free resources 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 Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 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 Senior | Next Rank: 100 Posts Joined 15 Jan 2018 Posted: 83 messages 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. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 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. 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. • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

### 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 Scott@TargetTestPrep

Target Test Prep

159 posts
2 Max@Math Revolution

Math Revolution

84 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

59 posts
4 Ian Stewart

GMATiX Teacher

46 posts
5 GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts