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# If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?

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If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

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19 May 2006, 11:27
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If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?

(1) a = 1
(2) b = 2

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-2-3x-c-x-a-x-b-for-all-x-what-is-the-105824.html
[Reveal] Spoiler: OA
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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

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19 May 2006, 11:43
C?

by subing both a and b. we get :

x^2 +3x + 2

set both sides equal and solve for c.
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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

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19 May 2006, 11:48
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x^2 + ax+bx + ab
a+b=3
c=ab

hence D
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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

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19 May 2006, 11:49
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yach wrote:
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2

It should be D

equation both the equation we get

x^2 + 3x + c = x^2 + (a+b)x + ab

which means a +b =3 and ab =c

from condition 1 we know a =1 so b =2 so c =2 sufficient
from condition 2 we know b =2 so a =1 so c =2 sufficient

hence D
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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

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19 May 2006, 12:00
yach wrote:
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2

x^2 + 3x + c = (x + a)(x + b)
x^2 + 3x + c = x^2 + xa + x b + ab
3x + c = x(a + b) + ab

here 3x = x(a + b) or a+b = 3, and c = ab
now each of the statement is suffcient to find the value of c.

so D.
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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

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19 May 2006, 12:39
I think I am getting worse in math day by day
Have exam on May 30th. good luck to me
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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

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22 Jul 2015, 23:59
Hello from the GMAT Club BumpBot!

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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

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23 Jul 2015, 01:53
yach wrote:
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?
(1) a = 1
(2) b = 2

Here, x^2 +3x +c=(x+a)(x+c)
or, x^2 +3x +c =x^2+x(a+b)+ab
or,3x+c=x(a+b)+ab
Now you can tell 3x = x(a+b), so c=ab

From statement 1, you never get the value of b. so it is insufficient.
From statement 2, you never get the value of a. so it is insufficient.
From the both statements you get the value of both a &b. so it is sufficient. a=1 & b=2 and ab=2
Again your taken condition 3x= x(a+b) is also fulfilled. just like 3x= x(1+2).
Thank you
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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink]

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23 Jul 2015, 02:37
yach wrote:
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?

(1) a = 1
(2) b = 2

Since $$x^2+3x+c=(x + a)(x + b)$$ is true "for ALL values of $$x$$" then it must hold true for $$x=0$$ too --> $$c=ab$$;

Next, substitute $$c=ab$$ --> $$x^2+3x+ab=x^2+bx+ax+ab$$ --> $$3x=bx+ax$$ --> again it must be true for $$x=1$$ too --> $$a+b=3$$.

So we have: $$c=ab$$ and $$a+b=3$$. Question: $$c=?$$

(1) $$a=1$$ --> as $$a+b=3$$ then $$b=2$$ and $$c=ab=2$$. Sufficient
(2) $$b=2$$ --> as $$a+b=3$$ then $$a=1$$ and $$c=ab=2$$. Sufficient.

Similar questions:
equation-ds-105823.html?hilit=constants#p768377

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-2-3x-c-x-a-x-b-for-all-x-what-is-the-105824.html
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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ?   [#permalink] 23 Jul 2015, 02:37
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