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Intern  B
Joined: 12 Jan 2019
Posts: 32
What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 59% (01:49) correct 41% (02:04) wrong based on 71 sessions

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What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?

A. -7
B. -3
C. -1
D. 3
E. 7

Originally posted by Nums99 on 02 Feb 2019, 06:24.
Last edited by Bunuel on 03 Feb 2019, 02:15, edited 1 time in total.
Renamed the topic and edited the question.
Director  G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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Nums99 wrote:
What is the value of b If 2x − 1 is a factor of 2x^2 +bx +3 ?
a) -7
b)-3
c)-1
d)3
e)7

If some expression is a factor of a quadratic equation, this means that it will satisfy it

2x-1=0

x=1/2

Put the value of x in the quadratic equation
1/2 + b/2 + 3 =0
b = -7
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Intern  B
Joined: 08 Oct 2017
Posts: 30
Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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Quadratic equation 2x^+bx+3 = 0

Factors (2x-1)*(2nd factor) = 2x^+bx+3= 0

(2x-1) = 0 ==>> x = 1/2

plug in value of x into quadratic equation to determine value of b. You can take it from here.

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Nums99 wrote:
What is the value of b If 2x − 1 is a factor of 2x^2 +bx +3 ?
a) -7
b)-3
c)-1
d)3
e)7

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RC Moderator V
Joined: 24 Aug 2016
Posts: 789
GMAT 1: 540 Q49 V16 GMAT 2: 680 Q49 V33 Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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According to the Q: 2x − 1 =0 ==>$$x=\frac{1}{2}$$
Hence $$b=-2x-\frac{3}{x}$$ =-1-3.2 = -7 Ans A

Just 1 point Nums99 .... in the Q you mentioned an expression not an equation.
To clarify : 2x^2 +bx +3 is an expression & on contracy 2x^2 +bx +3 =0 is an equation.
All the solutions are done assuming you mentioned an eqn: 2x^2 +bx +3 =0
If the Q is about only the expression .....in my view the Q does not stand _________________
Please let me know if I am going in wrong direction.
Thanks in appreciation.
Manager  G
Joined: 14 May 2018
Posts: 96
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 710 Q49 V38 GPA: 4
Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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1
Nums99 wrote:
What is the value of b If 2x − 1 is a factor of 2x^2 +bx +3 ?
a) -7
b)-3
c)-1
d)3
e)7

If 2x-1 is a factor, then it means that 2x-1=0 ==> x=1/2

Now put x=1/2 in the equation 2x^2+bx+3=0

2*1/4+1/2b+3=0
Solving, b=-7

Ans:A
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GMAT:710 (Q49,V38,IR8,AWA5)
Director  V
Joined: 12 Feb 2015
Posts: 917
Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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Nums99 wrote:
What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?

A. -7
B. -3
C. -1
D. 3
E. 7

If someone got stuck and could not proceed as per the solutions mentioned above then you may work backward; One could use answer options and substitute for the value of b. Since 2x-1 is a factor, you would realize that only option A works.
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Manish "Only I can change my life. No one can do it for me"
Senior Manager  S
Joined: 12 Sep 2017
Posts: 302
Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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CAMANISHPARMAR wrote:
Nums99 wrote:
What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?

A. -7
B. -3
C. -1
D. 3
E. 7

If someone got stuck and could not proceed as per the solutions mentioned above then you may work backward; One could use answer options and substitute for the value of b. Since 2x-1 is a factor, you would realize that only option A works.

Hello CAMANISHPARMAR !

Do you mean like this?

2x^2 - 7x + 3

2x^2 - 6x - x + 3

2x(x-3) -1(x-3)

(2x-1)(x-3)?

Thank you so much in advance!
Director  V
Joined: 04 Dec 2015
Posts: 743
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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jfranciscocuencag wrote:
CAMANISHPARMAR wrote:
Nums99 wrote:
What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?

A. -7
B. -3
C. -1
D. 3
E. 7

If someone got stuck and could not proceed as per the solutions mentioned above then you may work backward; One could use answer options and substitute for the value of b. Since 2x-1 is a factor, you would realize that only option A works.

Hello CAMANISHPARMAR !

Do you mean like this?

2x^2 - 7x + 3

2x^2 - 6x - x + 3

2x(x-3) -1(x-3)

(2x-1)(x-3)?

Thank you so much in advance!

Hi jfranciscocuencag,

Yes above method is correct.

Given $$(2x - 1)$$ is factor of $$(2x-1)(x-3)$$. Hence $$b = -7$$ will be the answer.

Director  V
Joined: 12 Feb 2015
Posts: 917
Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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jfranciscocuencag wrote:
CAMANISHPARMAR wrote:
Nums99 wrote:
What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?

A. -7
B. -3
C. -1
D. 3
E. 7

If someone got stuck and could not proceed as per the solutions mentioned above then you may work backward; One could use answer options and substitute for the value of b. Since 2x-1 is a factor, you would realize that only option A works.

Hello CAMANISHPARMAR !

Do you mean like this?

2x^2 - 7x + 3

2x^2 - 6x - x + 3

2x(x-3) -1(x-3)

(2x-1)(x-3)?

Thank you so much in advance!

Yes, you got it right. You will get 2x-1 as a factor only when b = -7
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Manish "Only I can change my life. No one can do it for me" Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?   [#permalink] 23 Feb 2019, 09:53
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