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x^2 + b x + c = (x + d) ^2

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by sanju09 » Sat Aug 14, 2010 4:53 am
If b, c, and d are constants and x^2 + b x + c = (x + d) ^2 for all values of x, what is the value of c?

(1) d = 3.
(2) b = 6.


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by kvcpk » Sat Aug 14, 2010 5:11 am
sanju09 wrote:If b, c, and d are constants and x^2 + b x + c = (x + d) ^2 for all values of x, what is the value of c?

(1) d = 3.
(2) b = 6.


[spoiler]Source: Picked from some source unknown to www.avenuesabroad.org[/spoiler]
x^2 + b x + c = (x + d) ^2
x^2 + b x + c = x^2 + 2dX + d^2
b=2d, c=d^2
(1) d = 3. implies c=9
Suff
(2) b = 6.
b=2d
hence d=3
implies c=9
SUFF

pick D
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by reply2spg » Sat Aug 14, 2010 5:14 am
D is right
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by gmatmachoman » Sat Aug 14, 2010 5:16 am
x^2 + b x + c = (x + d) ^2

x^2 + 2 Vc . x + c = x^2 + 2d.x + d^2

equating the coefficients : we can see that 2 Vc = 2d ; c = d^2

st 1 :

d = 3.

Vc = d
c = d^2
= 3^2 = 9

Sufficient

St 2: b = 6.

2Vc = b

2Vc =6
sqrt C = 3
C = 3^2
= 9

Sufficient

Pick D
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