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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

Respuesta :

Answer:

Option d

Step-by-step explanation:

given that a, b, c, and d be non-zero real numbers.

[tex]ax(cx + d) = -b(cx+d) \\acx^2+x(ad+bc)+bd =0[/tex]

we can factorise this equation by grouping

[tex](acx^2+xad)+)xbc+bd) =0\\ax(cx+d) +b(cx+d) =0\\(ax+b)(cx+d) =0[/tex]

Equate each factor to 0 to get

[tex]x=\frac{-b}{a} , \frac{-d}{c}[/tex]

Ratio of one solution to another would be

[tex]\frac{-b}{a} / \frac{-d}{c} \\=\frac{ad}{bc}[/tex]

So ratio would be ad/bc

Out of the four options given, option d is equal to this

So option d is right

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