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KarishmaB
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KarishmaB
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Let a,b,c, and d be nonzero 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?

A. \(-\frac{ab}{cd}\)
B. \(-\frac{ac}{bd}\)
C. \(-\frac{ad}{bc}\)
D. \(\frac{ab}{cd}\)
E. \(\frac{ad}{bc}\)


Having trouble with this problem and would appreciate if someone could walk me through a solution. Thanks!


\(ax(cx+d)=-b(cx+d)\)

You solve a quadratic by splitting it into factors.

\(ax(cx+d) + b(cx+d) = 0\)

But recognise that the factors are already there in this equation. Take (cx + d) common.
\((ax + b)*(cx + d) = 0\)

Roots are -b/a and -d/c

Their ratio could be bc/ad or ad/bc.

Answer (E)

Hi Karishma! Would you be able to suggest similar questions to practice? Thank you
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Here's my solution in handwritten form.
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KarishmaB
amitpaul527
Let a,b,c, and d be nonzero 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?

A. \(-\frac{ab}{cd}\)
B. \(-\frac{ac}{bd}\)
C. \(-\frac{ad}{bc}\)
D. \(\frac{ab}{cd}\)
E. \(\frac{ad}{bc}\)


Having trouble with this problem and would appreciate if someone could walk me through a solution. Thanks!


\(ax(cx+d)=-b(cx+d)\)

You solve a quadratic by splitting it into factors.

\(ax(cx+d) + b(cx+d) = 0\)

But recognise that the factors are already there in this equation. Take (cx + d) common.
\((ax + b)*(cx + d) = 0\)

Roots are -b/a and -d/c

Their ratio could be bc/ad or ad/bc.

Answer (E)

so helpful number for me
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My technique works but may not be the most time efficient.
Plug in numbers I chose a=5 b=1 c=2 d=3

I set everything equal to zero and had a weird quadratic and used quadratic formula and got -3/2 and -1/5 as solutions.

I set an equal denominator and got 15:2 as the ratio.

I scanned for which answer choice would give me the same ratio with the plugged in numbers from before and it was correct.
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