quadratic eqn

[gmatnmein2010]

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

[papgust]

I would go for D

A. d = 3

x^2 + bx + c = (x + 3)^2 = x^2 + 6x + 9.

c=9. Sufficient.

B. b = 6

x^2 + 6x + c = (x + d)^2

x^2 + 6x + c = x^2 + 2dx + d^2

2d = 6
d = 3

c = d^2 = 3^2 = 9
Sufficient.

[thephoenix]

IMO D
for DS in GMAT many a time a trick is hidden in the q itself
here for all values of X signifies x can be zero
in that case
x^2+bx+c=(x+d)^2--->c=d^2

s1) d=3--->c=d^2=9
suff

s2) b=6--->2d=6(when (x+d)^2 is expanded=x^2+2dx+d^2--->d=3--->c=9
suff

[shashank.ism]

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 --> bx+c = 2dx+d^2 --> (2d-b)X= 4d^2 - c this is true for all values of X
so if we put X=0, c= d^2
S1: D=3 so c= d^2 = 3^2=9. sufficient.
S2: if b= 6 , x^2 + 6x + c = x^2 + 2dx + d^2 --> so 2d=6 --> d=3 --> c=d^2 =9...............sufficient


I would go with D

[ajith]

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 + 2d + d^2

Comparing coefficients on both sides

b =2d
c= d^2

1.) d =3 ; c = d^2 = 9 sufficient
2) b =6; d =3 ; c = d^2 = 9; sufficient

D