Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Dec 1410:00 AM EST
-12:00 PM EST
Think a 100% GMAT Verbal score is out of your reach? Target Test Prep will make you think again! Our course uses techniques such as topical study and spaced repetition to maximize knowledge retention and make studying simple and fun.
Dec 1411:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.
Dec 1310:00 AM EST
-12:00 PM EST
Have you ever wondered how to score a PERFECT 805 on the GMAT? Meet Julia, a banking professional who used the Target Test Prep course to achieve this incredible feat. Julia's story is nothing short of an inspiration.- Dec 15
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Dec 1608:00 AM PST
-11:59 PM PST
GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes!- Dec 17
09:00 AM PST
-10:00 AM PST
Join Manhattan Prep instructor Whitney Garner for a fun—and thorough—review of logic-based (non-math) problems, with a particular emphasis on Data Sufficiency and Two-Parts. - Dec 18
10:00 AM PST
-11:00 AM PST
Here is the essential guide to securing scholarships as an MBA student! In this video, we explore the various types of scholarships available, including need-based and merit-based options.
08 Mar 2022, 05:30
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
87% (01:04) correct
13%
(00:56)
wrong
based on 62
sessions
History
Date
Time
Result
Not Attempted Yet
What are all of the roots of the equation \(x^3 = 3x^2 − 2x\) ?
(A) −3, 1, 2
(B) −2, 1, 3
(C) 0, 1, 2
(D) 0, 1
(E) 1, 2
(A) −3, 1, 2
(B) −2, 1, 3
(C) 0, 1, 2
(D) 0, 1
(E) 1, 2
08 Mar 2022, 07:50
Kudos
Bookmarks
Bunuel
What are all of the roots of the equation x³ = 3x² − 2x ?
(A) −3, 1, 2
(B) −2, 1, 3
(C) 0, 1, 2
(D) 0, 1
(E) 1, 2
(A) −3, 1, 2
(B) −2, 1, 3
(C) 0, 1, 2
(D) 0, 1
(E) 1, 2
STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
In this case, we can easily test the answer choices.
In fact, I can immediately see that x = 0 is a solution, since both sides of the equation would evaluate to be 0.
Let's go with that approach
When we plug x = 0 into the equation, we get: 0³ = 3(0)² − 2(0), which simplifies to be: 0 = 0. WORKS!
Since x = 0 is a solution to the given equation, we can eliminate answers choices A, B and E, since they don't list x = 0 as a possible solution.
This leaves us with answer choices C and D.
Both answer choices say that x = 1, which means x = 1 must be a solution. So we won't bother testing that value.
However, choice C says x = 2 is a solution, and choice D says x = 2 isn't a solution, so let's test x = 2
We get: 2³ = 3(2)² − 2(2), which simplifies to be: 8 = 8. WORKS!
Since x = 2 is a solution to the given equation, we can eliminate answer choices D
Answer: C
ALGEBRAIC APPROACH
Given: x³ = 3x² − 2x
Rearrange terms to get: x³ - 3x² + 2x = 0
Factor out x to get: x(x² - 3x + 2) = 0
Factor the expression in the parentheses to get: x(x - 1)(x - 2) = 0
At this point, we can see that the solutions are x = 0, x = 1 and x = 2
Answer: C
Moderator:
