Question

Find all zeroes of x^3-2x

Answer 1

`\large\boxed{x=-\sqrt2,\ x=0,\ x=\sqrt2}`

Explanation:

`x^3-2x=0\qquad\text{distributive}\\\\x(x^2-2)=0\iff x=0\ \vee\ x^2-2=0\\\\x^2-2=0\qquad\text{add 2 to both sides}\\\\x^2=2\to x=\pm\sqrt2`

Answer 2

You can factor out an x:

x (
`x^(2)` - 2)

Now set x equal to zero and the expression in the parentheses equal to zero

x = 0

`x^(2)  - 2 = 0`

We don't need to do anything to x = 0 because x is already isolated, but you can further isolate x in the equation:

x^2 - 2 = 0

To do this add 2 to both sides

x^2 = 2

Take the square root of both sides to completely isolate x

x = ± √2

The zeros are:

0 and ±√2

Hope this helped!

~Just a girl in love with Shawn Mendes