Describe each of the following set by listing the elements in the set:
{x ∈ ℚ | x(x2 – 2)(2x + 3) = 0}
{-15, -5, -3, -1, 1, 3, 5, 15}
{-2, -3/2, 0, 2}
{}
{-3/2, 0}

Question

Describe each of the following set by listing the elements in the set:
{x ∈ ℚ | x(x2 – 2)(2x + 3) = 0}
	{-15, -5, -3, -1, 1, 3, 5, 15}
	{-2, -3/2, 0, 2}
	{}
	{-3/2, 0}

geerky42 · Answer

Just start by solving $x(x^2-2)(2x-3)=0$

geerky42 · Answer

If $ab = 0$, then either $a=0$ or $b=0$.

You can apply same logic here

anonymous · Answer

how come people are one on the weekend??
everyone needs a mega break from learning,i just logged on tho check my page.
seams stress full.

dayakar · Answer

x=0 or 
$$x^{2}-2=0$$

$$x^{2}=2$$$$x = \sqrt{2}or-\sqrt{2}$$

dayakar · Answer

therefore
$$x={0.\sqrt{2},-\sqrt{2},3/2}$$

dayakar · Answer

verify ur options

geerky42 · Answer

I mean $x(x^2-2)(2x+3)=0$

anonymous · Answer

@dayakar I can see why you may have started with x=0; but, why did you also do x^2-2=0?

geerky42 · Answer

So solutions would be $0, ~\text-\sqrt2, \sqrt2, \text-3/2$

Now check which elements are in set $\mathbb Q$.

geerky42 · Answer

If $x(\color{red}{x^2-2})(\color{blue}{2x+3})=0$, then $x=0, ~\color{red}{x^2-2}=0, \text{ or }\color{blue}{2x+3}=0$

anonymous · Answer

Okay, that makes sense. I get it now.

anonymous · Answer

and sqrt can't be expressed as a quotient. so it's just 0,-3/2

geerky42 · Answer

You are correct.

anonymous · Answer

Thank you for the help. I just became your fan :)

geerky42 · Answer

No problem :)