GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 Feb 2020, 18:50

### 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

# If 2 + √3 is one root of the equation, [m]x^2 - ax + b = 0[/m], ......

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3256
If 2 + √3 is one root of the equation, [m]x^2 - ax + b = 0[/m], ......  [#permalink]

### Show Tags

Updated on: 26 Jun 2019, 02:42
00:00

Difficulty:

45% (medium)

Question Stats:

59% (01:49) correct 41% (02:10) wrong based on 70 sessions

### HideShow timer Statistics

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

_________________

Originally posted by EgmatQuantExpert on 19 Jun 2019, 05:44.
Last edited by EgmatQuantExpert on 26 Jun 2019, 02:42, edited 1 time in total.
Intern
Joined: 27 Jun 2018
Posts: 14
Re: If 2 + √3 is one root of the equation, [m]x^2 - ax + b = 0[/m], ......  [#permalink]

### Show Tags

19 Jun 2019, 10:30
3
1
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)
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5918
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If 2 + √3 is one root of the equation, [m]x^2 - ax + b = 0[/m], ......  [#permalink]

### Show Tags

19 Jun 2019, 10:36
giving a try
$$x^2 - ax + b = 0$$,
so
we have ; (2+√3)^2- (2+√3)a+b=0
now value of a,b has to be such that eqn is 0
so let a= 4 and b=1
we get
7+4√3-8-4√3+1=0
sufficient
a+b = 4+1 ; 5
IMO E

EgmatQuantExpert wrote:
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

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3256
Re: If 2 + √3 is one root of the equation, [m]x^2 - ax + b = 0[/m], ......  [#permalink]

### Show Tags

26 Jun 2019, 02:44

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.

_________________
VP
Joined: 20 Jul 2017
Posts: 1332
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If 2 + √3 is one root of the equation, [m]x^2 - ax + b = 0[/m], ......  [#permalink]

### Show Tags

26 Jun 2019, 03:53
EgmatQuantExpert wrote:
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

If 1 root is x + sqrt(y)
The other root will be x - sqrt(y)

So other root is 2 - 3^1/2

a = sum of roots = 4
b = product of roots = 4 - 3 = 1

a + b = 5

Option E

Posted from my mobile device
Re: If 2 + √3 is one root of the equation, [m]x^2 - ax + b = 0[/m], ......   [#permalink] 26 Jun 2019, 03:53
Display posts from previous: Sort by

# If 2 + √3 is one root of the equation, [m]x^2 - ax + b = 0[/m], ......

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne