If there is exactly one root of the equation x^2 + ax + b : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 26 Feb 2017, 08:51

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If there is exactly one root of the equation x^2 + ax + b

Author Message
TAGS:

### Hide Tags

Intern
Joined: 19 Sep 2010
Posts: 15
Followers: 0

Kudos [?]: 30 [0], given: 4

If there is exactly one root of the equation x^2 + ax + b [#permalink]

### Show Tags

23 Aug 2011, 22:17
1
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:25) correct 26% (01:18) wrong based on 42 sessions

### HideShow timer Statistics

If there is exactly one root of the equation x^2 + ax + b, where a and b are positive constants, what is b in terms of a?

A. a/2
B. a
C. 3a/2
D. a^2/2
E. a^2/4

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-there-is-exactly-one-root-of-the-equation-x-2-ax-b-128527.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 13 Jul 2013, 07:00, edited 2 times in total.
Renamed the topic and edited the question.
VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1420
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75
Followers: 177

Kudos [?]: 1367 [0], given: 62

Re: Inequalities, how to crack solve this [#permalink]

### Show Tags

23 Aug 2011, 22:48
i guess the source is manhattan...anywayz
i got struck with a simple technique...picking up numbers..
consider (x+1)^2=x^2+2x+1
(x+2)^2=x^2+4x+4
....similarly u can go for other numbers as well..then analyse the values of a and b by considering the given options..
ans e
_________________
Intern
Joined: 04 May 2011
Posts: 11
Followers: 0

Kudos [?]: 3 [0], given: 11

Re: Inequalities, how to crack solve this [#permalink]

### Show Tags

23 Aug 2011, 23:06
$$x^2+ax+b$$ => has only 1 solution
So the equation should be of the form $$x^2 + 2Bx + B^2=0$$ (i.e) $$(x+B)^2=0$$ OR $$x^2 - 2Bx + B^2=0$$ (i.e) $$(x-B)^2=0$$
Hence substitute in place of B^2 = b and in place of 2B = a
we get a=2$$\sqrt{b}$$
=> $$a^2=4b$$ [Squaring on both sides]
=> $$b=a^2/4$$
(E)

Hope this helps !
Intern
Joined: 19 Sep 2010
Posts: 15
Followers: 0

Kudos [?]: 30 [0], given: 4

Re: Inequalities, how to crack solve this [#permalink]

### Show Tags

23 Aug 2011, 23:11
how did you take a=2sqrtb, from the above equation ?
Intern
Joined: 04 May 2011
Posts: 11
Followers: 0

Kudos [?]: 3 [0], given: 11

Re: Inequalities, how to crack solve this [#permalink]

### Show Tags

24 Aug 2011, 00:47
naaga wrote:
how did you take a=2sqrtb, from the above equation ?

Since the given equation is a quadratic equation, there would always be 2 roots (solution) for it. eg: (x+p)(x+q)
But the question says the equation has only 1 solution. This could be possible only when both the roots are same. i.e (x+p)(x+p).
This can be written as $$(x+p)^2$$
We know the formula for this i.e $$(x+p)^2 = x^2+2px+p^2$$
Now visualize the given equation ($$x^2+ax+b$$) with the above formula:
Coefficient of $$x^2$$ = 1
Coefficient of $$x$$ = a (which is nothing but 2p)
Constant term (i.e the $$p^2$$) = b
Hence we can write:
$$p^2=b$$
=> $$p=\sqrt{b}$$
=> a=2p = $$2\sqrt{b}$$
Intern
Joined: 19 Sep 2010
Posts: 15
Followers: 0

Kudos [?]: 30 [0], given: 4

Re: Inequalities, how to crack solve this [#permalink]

### Show Tags

24 Aug 2011, 02:36
thank you srivats212, nice explanation.
Manager
Joined: 04 Apr 2010
Posts: 162
Followers: 1

Kudos [?]: 182 [0], given: 31

Re: Inequalities, how to crack solve this [#permalink]

### Show Tags

24 Aug 2011, 11:31
the root must be -a/2. (Quadratic equation with only one root)
Substituting the -a/2 in the equation & equating it to 0.
You will get b= a^2 / 4
_________________

Consider me giving KUDOS, if you find my post helpful.
If at first you don't succeed, you're running about average. ~Anonymous

Director
Joined: 01 Feb 2011
Posts: 755
Followers: 14

Kudos [?]: 119 [0], given: 42

Re: Inequalities, how to crack solve this [#permalink]

### Show Tags

24 Aug 2011, 20:02
one root for a quadratic equation ax^2+bx+c is possible only when b^2 = 4ac ---1

Here b = a
c= b
a = 1

substituting these values in 1, we have

a^2 = 4b => b =a^2/4

Intern
Joined: 31 May 2010
Posts: 38
Followers: 0

Kudos [?]: 2 [0], given: 2

Re: Inequalities, how to crack solve this [#permalink]

### Show Tags

26 Aug 2011, 05:16
Can be possible only when determinent = 0

therefore, b ^2 - 4ac= 0
b=a , a=1 and c=b. After substituting values we will get a^2 - 4 (1)(b)=0 =>a ^2 =4b =>b= a^2/4.
Re: Inequalities, how to crack solve this   [#permalink] 26 Aug 2011, 05:16
Similar topics Replies Last post
Similar
Topics:
5 If 'a' and 'b' are the roots of the quadratic equation x^2 - x + 1 = 0 3 12 Sep 2015, 10:14
There are 2 equations x^2+ax+c and x^2+bx +a 3 23 Oct 2013, 06:04
9 If there is exactly one root of the equation x^2 + ax + b 9 03 Mar 2012, 17:14
15 If equation 3x-2y=5 and ax+6y=10 have no common root, a=? 9 15 Aug 2011, 02:21
20 If one root of x^2+px+12=0 is 4, and the equation x^2+px+q=0 12 09 Dec 2010, 06:39
Display posts from previous: Sort by