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06 Aug 2007, 11:29
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If b, c, and d are constants and x2 + bx + c = (x + d)2 for all values of x, what is the value
of c?
(1) d = 3
(2) b = 6
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
of c?
(1) d = 3
(2) b = 6
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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06 Aug 2007, 11:57
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smily_buddy
Ans. - C
Given x^2 + b.x + c = (x + d) ^2
explanding this eq'n we get ,
x^2 + b.x + c = x ^2 + 2.x.d + d ^2
b.x + c = 2.x.d + d ^2 ---------------------1
St-1 . d=3
putting this in 1,
b.x + c = 6x + 9
We have 2 variables left, x and b. Hence in suff.
St2 : b = 6
Putting this in 1 we will again be left with 2 var d and x.
Using both together,
we get c = 9
Hence C.
06 Aug 2007, 15:59
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smily_buddy
See the sum of the roots of an equation ax^2 + bx + c is given by the formula -b/a and the product of the roots is given is c/a
Here we know both the roots are -d
so -b/a = -2d and c/a = d^2. Now remember in the problem a = 1.
so -b = -2d and c = d^2
If d or b is given we can find C. That is what stmts 1 and 2 do. HTH
