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

 It is currently 16 Jan 2019, 15:20

### 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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# What is the product of all roots of the equation (x

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6804
GMAT 1: 760 Q51 V42
GPA: 3.82
What is the product of all roots of the equation (x  [#permalink]

### Show Tags

Updated on: 16 Jan 2018, 10:09
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:26) correct 25% (01:23) wrong based on 221 sessions

### HideShow timer Statistics

[GMAT math practice question]

What is the product of all roots of the equation $$(x+1)^2=|x+1|$$?

$$A. -2$$
$$B. -1$$
$$C. 0$$
$$D. 1$$
$$E. 2$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 16 Jan 2018, 01:27. Last edited by Bunuel on 16 Jan 2018, 10:09, edited 1 time in total. Edited the OA. Math Expert Joined: 02 Aug 2009 Posts: 7199 Re: What is the product of all roots of the equation (x [#permalink] ### Show Tags 16 Jan 2018, 06:02 1 1 MathRevolution wrote: [GMAT math practice question] What is the product of all roots of the equation $$(x+1)^2=|x+1|$$? $$A. -2$$ $$B. -1$$ $$C. 0$$ $$D. 1$$ $$E. 2$$ Hi... you are required to relook into the OA.. $$(x+1)^2=|x+1|$$ at the first look will give 0 as a root.. x as 0 will make the equation... $$(x+1)^2=|x+1|........(0+1)^2=|0+1|....1=1$$ so product of all roots irrespective of other roots will remain ZERO C.. if you want to solve it.. when x+1 is negative.. $$(x+1)^2=|x+1|............x^2+2x+1=-x-1......x^2+3x+2=0.......(x+2)(x+1)=0$$ roots are -2 and -1 when x+1 is positive.. $$(x+1)^2=|x+1|............x^2+2x+1=x+1......x^2+x=0.......x(x+1)=0$$ roots are 0 and -1... product : 0*-1*-2=0 C _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor CEO Joined: 11 Sep 2015 Posts: 3323 Location: Canada Re: What is the product of all roots of the equation (x [#permalink] ### Show Tags 16 Jan 2018, 07:46 1 Top Contributor 2 MathRevolution wrote: [GMAT math practice question] What is the product of all roots of the equation $$(x+1)^2=|x+1|$$? $$A. -2$$ $$B. -1$$ $$C. 0$$ $$D. 1$$ $$E. 2$$ There are 3 steps to solving equations involving ABSOLUTE VALUE: 1. Apply the rule that says: If |x| = k, then x = k and/or x = -k 2. Solve the resulting equations 3. Plug solutions into original equation to check for extraneous roots Given: (x + 1)² = | x + 1| Apply rule to get two equations: (x + 1)² = x + 1 and -(x + 1)² = x + 1 Take: (x + 1)² = x + 1 Expand and simplify left side: x² + 2x + 1 = x + 1 Set this quadratic equation to equal zero: x² + x = 0 Factor to get: x(x + 1) = 0 So, x = 0 and x = -1 are two solutions (aka roots) of the original equation When we test these two solutions, we find that they BOTH work. IMPORTANT: At this point, we COULD solve -(x + 1)² = x + 1 for x also. HOWEVER, doing so would be a waste of time since the questions asks us to find the PRODUCT of all possible solutions. Since x = 0 is one of the solutions, we can be sure that the product will be 0 Answer: C RELATED VIDEO _________________ Test confidently with gmatprepnow.com Intern Joined: 20 Aug 2017 Posts: 26 Re: What is the product of all roots of the equation (x [#permalink] ### Show Tags 16 Jan 2018, 10:05 1 I think OA should be C instead of D. Math Expert Joined: 02 Sep 2009 Posts: 52161 Re: What is the product of all roots of the equation (x [#permalink] ### Show Tags 16 Jan 2018, 10:10 sghoshgt wrote: I think OA should be C instead of D. Yes, you are right, it's C. Edited. Thank you. _________________ Intern Joined: 01 Jun 2015 Posts: 41 Location: India Re: What is the product of all roots of the equation (x [#permalink] ### Show Tags 16 Jan 2018, 10:29 1 Consider x+1 = A so A^2 = |A| Squaring both the sides A^4 = A^2 ( this will always be positive ) A^4 - A^2 = 0 A^2 ( A^2 - 1 ) = 0 A=0,1,-1 Product of roots = 0 SVP Joined: 26 Mar 2013 Posts: 1998 Re: What is the product of all roots of the equation (x [#permalink] ### Show Tags 17 Jan 2018, 03:03 saraheja wrote: Consider x+1 = A so A^2 = |A| Squaring both the sides A^4 = A^2 ( this will always be positive ) A^4 - A^2 = 0 A^2 ( A^2 - 1 ) = 0 A=0,1,-1 Product of roots = 0 While The answer is correct, you must return to original equation you have (x+1=A) to find values of x. It is not not about A. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6804 GMAT 1: 760 Q51 V42 GPA: 3.82 What is the product of all roots of the equation (x [#permalink] ### Show Tags 18 Jan 2018, 00:42 => Now, $$(x+1)^2=|x+1|$$ $$⇔ |x+1|^2=|x+1|$$ $$⇔ |x+1|^2-|x+1|= 0$$ $$⇔ |x+1|(|x+1|-1) = 0$$ $$⇔ |x+1| = 0$$ or $$|x+1| = 1$$ $$⇔ x = -1$$ or $$x+1 = ±1$$ $$⇔ x = -1$$ or $$x = -1 ±1$$ $$⇔ x = -1, x= -2$$ or $$x = 0$$ The product of these solutions is $$(-1)*(-2)*0 = 0$$. Therefore, the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

What is the product of all roots of the equation (x &nbs [#permalink] 18 Jan 2018, 00:42
Display posts from previous: Sort by