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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] New post 19 May 2006, 10:27
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D
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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] New post 19 May 2006, 10:43
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] New post 19 May 2006, 10:48
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] New post 19 May 2006, 10:49
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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

Please explain your answer. Thanks


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] New post 19 May 2006, 11:00
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] New post 19 May 2006, 11:39
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] New post 22 Jul 2015, 22:59
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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink] New post 23 Jul 2015, 00:53
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

Please explain your answer. Thanks

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 :evil:

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 :roll:
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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c ? [#permalink] New post 23 Jul 2015, 01:37
Expert's post
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.

Answer: D.

Similar questions:
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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, 01:37
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