Question

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?

Answer 1

`x_1=-\frac{b}a,x_2=-\frac{d}c`

Explanation:

Solving for x:

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

In this form is easy to identify the factors of the quadratic function:
`(ax+b)(cx+d)`. The two solutions are the values ​​that make each of the factors equals to zero.

`ax_1+b=0\\ax_1=-b\\x_1=-\frac{b}a\\cx_2+d=0\\cx_2=-d\\x_2=-\frac{d}c`