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 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.
05 Dec 2010, 14:28
Kudos
Bookmarks
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
59% (01:14) correct
41%
(01:28)
wrong
based on 296
sessions
History
Date
Time
Result
Not Attempted Yet
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2
(1) a = 1
(2) b = 2
05 Dec 2010, 14:51
Kudos
Bookmarks
ajit257
If x2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2
(1) a = 1
(2) b = 2
Since \(x^2+3x+c=(x + a)(x + b)\) is true "for ALL values of \(x\)" then it must hold true for \(x=0\) too --> \(c=ab\);
Next, substitute \(c=ab\) --> \(x^2+3x+ab=x^2+bx+ax+ab\) --> \(3x=bx+ax\) --> again it must be true for \(x=1\) too --> \(a+b=3\).
So we have: \(c=ab\) and \(a+b=3\). Question: \(c=?\)
(1) \(a=1\) --> as \(a+b=3\) then \(b=2\) and \(c=ab=2\). Sufficient
(2) \(b=2\) --> as \(a+b=3\) then \(a=1\) and \(c=ab=2\). Sufficient.
Answer: D.
Similar questions:
equation-ds-105823.html?hilit=constants#p768377
equating-coefficients-in-a-quadratic-equation-103919.html
Hope it's clear.
General Discussion
06 Dec 2010, 22:47
Kudos
Bookmarks
ajit257
If x2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2
(1) a = 1
(2) b = 2
Any expression of the form \((x + a)(x + b)\) can be expressed as \(x^2 + (a+b)x + ab\).
Comparing this with the quadratic equation containing c, \(a+b = 3\) and \(ab = c\).
So if the value of either \(a\) or \(b\) is known the value of other can be found out from \(a+b = 3\), and putting the two values in \(ab = c\), value of \(c\) can be found out.
Answer D.
