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If b, c, and d are constants and x^2 + bx + c = (x +

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If b, c, and d are constants and x^2 + bx + c = (x + [#permalink]

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If b, c, and d are constants and \(x^2 + bx + c = (x + d)^2\) for all values of x, what is the value of c?

(1) d = 3
(2) b = 6
[Reveal] Spoiler: OA
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Re: If b, c, and d are constants and x^2 + bx + c = (x + [#permalink]

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New post 05 Aug 2011, 06:21
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Galiya wrote:
If b, c, and d are constants and \(x^2 + bx + c = (x + d)^2\) for all values of x, what is the value
of c?
(1) d = 3
(2) b = 6

[Reveal] Spoiler: Comment
I got A instead of OA D
could you explain me please why it so?


ok here is what i think is the reasoning ...

expand the eqn .. \(x^2 + bx + c = x^2 + 2dx + d^2\)

cancelling the first term and comparing like terms we get

\(bx = 2dx << i.e. >>

b=2d\)

and \(c = d^2\)

now check the options we'd get both A and B to suffice ....
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Re: If b, c, and d are constants and x^2 + bx + c = (x + [#permalink]

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New post 05 Aug 2011, 06:32
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Galiya wrote:
If b, c, and d are constants and \(x^2 + bx + c = (x + d)^2\) for all values of x, what is the value
of c?
(1) d = 3
(2) b = 6


\(x^2 + bx + c = (x + d)^2\)

\(x^2 + bx + c = x^2 + d^2 + 2xd\) {:Note: (a+b)^2=a^2+b^2+2ab}

\(bx + c = d^2 + 2xd\) {:Note: (a+b)^2=a^2+b^2+2ab}


(1) d=3

\(bx + c = 9 + 6x\)

LHS=RHS for all x;

So, for x=0

\(b*0 + c = 9 + 6*0\)

\(c = 9\)

Sufficient.

(2) b=6

\(bx + c = d^2 + 2xd\)

LHS=RHS for all x;

So, for x=0

\(c=d^2\)----------1

for x=1

\(b + c = d^2 + 2d\)---------2

Using 1 and 2:
\(b = 2d\)

\(6=2d\)

\(d=3\)

Using 1:
\(c=d^2=3^2=9\)
Sufficient.

Ans: "D"
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Re: If b, c, and d are constants and x^2 + bx + c = (x + [#permalink]

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New post 03 Mar 2015, 20:49
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Re: If b, c, and d are constants and x^2 + bx + c = (x + [#permalink]

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New post 08 Nov 2016, 04:29
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If b, c, and d are constants and x^2 + bx + c = (x + [#permalink]

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New post 12 Sep 2017, 04:27
fortunetellerz wrote:
Galiya wrote:
If b, c, and d are constants and \(x^2 + bx + c = (x + d)^2\) for all values of x, what is the value
of c?
(1) d = 3
(2) b = 6

[Reveal] Spoiler: Comment
I got A instead of OA D
could you explain me please why it so?


ok here is what i think is the reasoning ...

expand the eqn .. \(x^2 + bx + c = x^2 + 2dx + d^2\)

cancelling the first term and comparing like terms we get

\(bx = 2dx << i.e. >>

b=2d\)

and \(c = d^2\)

now check the options we'd get both A and B to suffice ....


Good to know - thanks. I forgot this strategy while solving the question.
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Re: If b, c, and d are constants and x^2 + bx + c = (x +   [#permalink] 12 Sep 2017, 04:27
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