Question

How do you solve `x^4(x-2)>=0` using a sign chart?

Answer 1

The answer is `x in [2, +oo[`

Explanation:

Let `f(x)=x^4(x-2)`

The domain of `f(x)` is `D_f(x)=RR`

`AA x in RR, x^4>=0`

The sign chart is very simple

`color(white)(aaaa)` `x` `color(white)(aaaaaa)` `-oo` `color(white)(aaaaaa)` `2` `color(white)(aaaaaa)` `+oo`

`color(white)(aaaa)` `x-2` `color(white)(aaaaaaa)` `-` `color(white)(aaaaaaa)` `+`

`color(white)(aaaa)` `f(x)` `color(white)(aaaaaaaa)` `-` `color(white)(aaaaaaa)` `+`

Therefore,

`f(x)>=0`, when `x in [2, +oo[`