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

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Intern
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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Updated on: 03 Feb 2019, 02:15
3
1
00:00

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.
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Posts: 994
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Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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02 Feb 2019, 06:58
3
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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Joined: 08 Oct 2017
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Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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02 Feb 2019, 08:57
1

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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Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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02 Feb 2019, 10:33
1
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
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Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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02 Feb 2019, 11:25
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)
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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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20 Feb 2019, 09:31
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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Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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22 Feb 2019, 14:38
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!
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Re: What is the value of b If 2x − 1 is a factor of 2x^2 + bx + 3 ?  [#permalink]

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23 Feb 2019, 06:09
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.

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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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23 Feb 2019, 09:53
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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