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

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Senior Manager
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If x^2 + 3x + c = (x + a)(x + b) for all x, what is the [#permalink]  30 Apr 2006, 07:07
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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
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Ans Is D

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

a+b=3 , c=ab

1) a=1
1+b=3=>b=2 c=2----sufficient

2) b=2
a+2=3
a=1 =>c=2----sufficient
VP
Joined: 29 Apr 2003
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Agreed its D!!

Compare the values of the coefficients on LHS to the ones on RHS!

Y get a+b =3
and c= ab

U can get the avlues of both a and b from each of the given data!

Hence, u can compute the value of ab, thus c!
Senior Manager
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OA is 'D'. Nice work guys.
VP
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Good question... I like your questions.. keep them rolling!
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x^2 + x(b+a)+ab = x^2 + 3x + c

c = ab
3 = (b+a)

St1:

a = 1, then b = 2 and c = ab = 2. Sufficient.

St2:

b = 2, a = 1 and c = ab = 2. Sufficient.

Ans D
Manager
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Agree with D
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