GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
What is the product of all roots of the equation
[#permalink]
10 Mar 2021, 09:43
10 Mar 2021, 09:43
Expert Reply
1
Bookmarks
00:00
Question Stats:
84% (01:04) correct
16% (02:14) wrong based on 25 sessions
Hide Show timer Statistics
What is the product of all roots of the equation \((x+1)^2=|x+1|\)?
\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: What is the product of all roots of the equation
[#permalink]
10 Mar 2021, 10:15
10 Mar 2021, 10:15
1
Carcass wrote:
What is the product of all roots of the equation \((x+1)^2=|x+1|\)?
\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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
Re: What is the product of all roots of the equation
[#permalink]
10 Mar 2021, 10:25
10 Mar 2021, 10:25
1
Test for 0 first; if it is a root, then the product must be zero:
(x+1)^2 = x+1 --> 0+1 = 0+1
The answer is C.
Posted from my mobile device
(x+1)^2 = x+1 --> 0+1 = 0+1
The answer is C.
Posted from my mobile device
