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

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If x^2 + 3x + c = (x + a)(x + b) for all x, what is the [#permalink]  19 May 2006, 10:27
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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

Manager
Joined: 14 Mar 2006
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C?

by subing both a and b. we get :

x^2 +3x + 2

set both sides equal and solve for c.
Director
Joined: 16 Aug 2005
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x^2 + ax+bx + ab
a+b=3
c=ab

hence D
Manager
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Re: DS [#permalink]  19 May 2006, 10:49
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: DS [#permalink]  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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I think I am getting worse in math day by day
Have exam on May 30th. good luck to me
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