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

Option d

Step-by-step explanation:

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

we can factorise this equation by grouping

Equate each factor to 0 to get

Ratio of one solution to another would be

So ratio would be ad/bc

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

So option d is right

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.