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)
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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