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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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Joined: 02 Sep 2009
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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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New post 01 Nov 2018, 00:10
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

45% (01:35) correct 55% (01:36) wrong based on 48 sessions

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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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New post 01 Nov 2018, 01:29
Bunuel wrote:
If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c?

(1) a = 1
(2) a and b are positive inte


Question: c = ?

Given:\(x^2 + 3x + c = (x + a)(x + b)\)
i.e. \(x^2 + 3x + c = x^2 + (a+b)x + ab\)
Comparing the RHS with LHS we get,
\(a+b = 3\) and \(a*b = c\)


Now we have one linear relation between a and b and we need to find a*b to find c

Question REPHRASED: What is the value of a or b or c?

Statement 1: a = 1

SUFFICIENT

Statement 2: a and b are positive inters
i.e. a and b must be 1 and 2 only hence
c = 1*2 = 2
SUFFICIENT

Answer: Option 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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New post 03 Nov 2018, 01:50
Dear Moderator,

Please move to number properties

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Re: If x^2 + 3x + c = (x + a)(x + b) for all x, what is the value of c?   [#permalink] 03 Nov 2018, 01:50
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