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.
Nov 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
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. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
![If 2 + √3 is one root of the equation, [m]x^2 - ax + b = 0[/m], ......](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "If 2 + √3 is one root of the equation, [m]x^2 - ax + b = 0[/m], ......"){kind=icon}
Updated on: 26 Jun 2019, 03:42
Originally posted by EgmatQuantExpert on 19 Jun 2019, 06:44.
Last edited by EgmatQuantExpert on 26 Jun 2019, 03:42, edited 1 time in total.
Last edited by EgmatQuantExpert on 26 Jun 2019, 03:42, edited 1 time in total.
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
65% (01:56) correct
35%
(02:29)
wrong
based on 454
sessions
History
Date
Time
Result
Not Attempted Yet
If 2 + √3 is one root of the equation, \(x^2 - ax + b = 0\), where a, b are positive numbers, then what is the value of a + b?
- (A) 0
(B) 1
(C) 2√3
(D) 4
(E) 5
19 Jun 2019, 11:30
Kudos
Bookmarks
If one root of the quadratic equation is \(2+\sqrt{3},\)the other root is \(2-\sqrt{3}.\)Now, sum of roots = a = \(2+\sqrt{3}+2-\sqrt{3}\) = 4
product of roots = b = \((2+\sqrt{3})(2-\sqrt{3})\)= \(2^2 -{\sqrt{3}}^2\) = 4-3 = 1
Hence, a + b = 4 + 1 = 5 (Option E)
product of roots = b = \((2+\sqrt{3})(2-\sqrt{3})\)= \(2^2 -{\sqrt{3}}^2\) = 4-3 = 1
Hence, a + b = 4 + 1 = 5 (Option E)
26 Jun 2019, 03:44
Kudos
Bookmarks
Solution
Given:
- • 2 + √3 is one root of the quadratic equation, \(x^2 - ax + b = 0\)
• a, b are positive numbers
To find:
- • The value of a + b
Approach and Working Out:
- • We are given that 2 + √3 is one root of the quadratic equation, \(x^2 - ax + b = 0\)
• And, we know that, if a +√ b is one root of a quadratic equation, then the other root will be a - √b.
- o Thus, 2 + √3, and 2 - √3 are the two roots
• Now, from the given quadratic equation, \(x^2 - ax + b = 0\)
- o Sum of the roots = -(-a) = a = (2 + √3) + (2 - √3) = 4
o Product of the roots = b = (2 + √3) * (2 - √3) = 4 – 3 = 1
• Therefore, a + b = 4 + 1 = 5
Hence, the correct answer is Option E.
Answer: E
