Let a, b, c, and d be non-zero real numbers. If the quadratic equation ax(cx + d) = -b(cx+d) is solved for x, which of the following is a possible ratio of the 2 solutions?
(1) -ab/cd
(2) -ac/bd
(3) -ad/bc
(4) ab/cd
(5) ad/bc
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Ratio of 2 solutions - GMAT Exam pack 2
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GMATGuruNY
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ax(cx + d) = -b(cx+d)prata wrote:Let a, b, c, and d be non-zero real numbers. If the quadratic equation ax(cx + d) = -b(cx+d) is solved for x, which of the following is a possible ratio of the 2 solutions?
(1) -ab/cd
(2) -ac/bd
(3) -ad/bc
(4) ab/cd
(5) ad/bc
ax(cx+d) + b(cx+d) = 0.
(cx+d)(ax+b) = 0.
The resulting equation is valid only if cx+d = 0 or ax+b = 0.
Root one:
cx+d = 0
cx = -d
x = -(d/c).
Root two:
ax+b = 0
ax = -b
x = -(b/a)
(root one)/(root two):
-(d/c)/-(b/a) = (d/c) * (a/b) = ad/bc.
The correct answer is E.
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Scott@TargetTestPrep
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ax(cx + d) = -b(cx + d)Let a, b, c, and d be non-zero real numbers. If the quadratic equation ax(cx + d) = -b(cx+d) is solved for x, which of the following is a possible ratio of the 2 solutions?
(1) -ab/cd
(2) -ac/bd
(3) -ad/bc
(4) ab/cd
(5) ad/bc
ax(cx + d) + b(cx + d) = 0
Next we can factor out (cx + d):
(cx + d)(ax + b) = 0
Using the zero product property, we can set the expression in each set of parentheses to zero:
cx + d = 0
cx = -d
x = -d/c
Or
ax + b = 0
ax = -b
x = -b/a
So a possible ratio is:
(-d/c)/(-b/a)
ad/bc
Answer:E
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Matt@VeritasPrep
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I think I've got a quicker way.
Suppose we have
ax(cx + d) = -b(cx+d)
If (cx + d) ≠ 0, then we can divide both sides by (cx + d), leaving us
ax = -b
x = -b/a
But if (cx + d) does = 0, then we have cx + d = 0, or x = -d/c.
That gives us our two solutions, the ratio for which is
(-b/a) / (-d/c)
or
bc/ad
This is the same as E, so we're set.
Suppose we have
ax(cx + d) = -b(cx+d)
If (cx + d) ≠ 0, then we can divide both sides by (cx + d), leaving us
ax = -b
x = -b/a
But if (cx + d) does = 0, then we have cx + d = 0, or x = -d/c.
That gives us our two solutions, the ratio for which is
(-b/a) / (-d/c)
or
bc/ad
This is the same as E, so we're set.
