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Quadratic match

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by maihuna » Fri Nov 13, 2009 12:32 pm
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]E/D[/spoiler]
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Source: — Data Sufficiency |

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Re: Quadratic match

by Ian Stewart » Fri Nov 13, 2009 1:11 pm
maihuna 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?
If x^2 + bx + c = (x + d)^2 for *all* values of x, then the equation is certainly true when x=0. Plugging in, we find that c = d^2. So Statement 1 is sufficient.

Now, expanding the right side, and replacing c with d^2:

x^2 + bx + d^2 = x^2 + 2dx + d^2
bx = 2dx
b = 2d

So if we know b, we can find d, and therefore find c, and Statement 2 is also sufficient.
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by Lance123 » Fri Nov 13, 2009 9:35 pm
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


Is it possible to look at it from this point of view.

Taking statement 1 Alone:
d=3

x^2 + bx + c = (x + d)^2 , d=3
x^2 + bx + c = (x + 3)^2
expanding the RHS and comparing coefficients, it is possible to determine c

So 1 is sufficient.

Taking statement 2
b = 6
x^2 + bx + c = (x + d)^2

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

comparing coefficients,

2d=6
d=3

c= d^2
c= (3)^2
c=9

Statement 2 is Sufficient.
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by notts5 » Sun Nov 15, 2009 1:08 am
But we know by comparing the two sides that c=d^2 and Statement one provides us with the value of d=3.

Therefore, c=d^2=(3)^2=9

Hence, Statement 1 is sufficient.
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