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

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Manager
Joined: 16 Jan 2011
Posts: 102
If b, c, and d are constants and x^2 + bx + c = (x + [#permalink]

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05 Aug 2011, 06:16
1
7
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Difficulty:

75% (hard)

Question Stats:

45% (01:03) correct 55% (01:22) wrong based on 217 sessions

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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
Intern
Status: If I play my cards right, I can work this to my advantage
Joined: 18 Jul 2011
Posts: 14
Location: India
Concentration: Operations, Social Entrepreneurship
GMAT Date: 11-12-2011
WE: Information Technology (Telecommunications)
Re: If b, c, and d are constants and x^2 + bx + c = (x + [#permalink]

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05 Aug 2011, 07:21
2
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

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 ....
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1901
Re: If b, c, and d are constants and x^2 + bx + c = (x + [#permalink]

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05 Aug 2011, 07:32
1
3
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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Manager
Joined: 30 Jul 2014
Posts: 145
GPA: 3.72
Re: If b, c, and d are constants and x^2 + bx + c = (x + [#permalink]

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12 Sep 2017, 05:27
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

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, 05:27
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# If b, c, and d are constants and x^2 + bx + c = (x +

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