Question

Describe each of the following set by listing the elements in the set:
{x ∈ ℚ | x(x2 – 4)(2x + 3) = 0}

Answer 1

@mathmate hey can you work through this with me? the answer is supposed to be {-2, -3/2, 0, 2} and i got 4 :(

Answer 2

@kropot72

Answer 3

@freckles

Answer 4

We need to use the zero product property
(see for example https://www.mathsisfun.com/algebra/zero-product-property.html )

If (x^2-4)x=0, which can be factored as
(x+2)(x-2)x=0.
Using the zero product property, then
(x+2)=0, or
(x-2)=0, or
x=0
(note: the or's above are inclusive or's, meaning and/or ).
So if (x+2)=0, then x=-2,
if (x-2)=0, then x=2
if x=0, then x=0.

Apply the zero product property to your problem and you'll get the correct answers.