Question

How do you solve `4x^2-8x>=0` using a sign chart?

Answer 1

The answer is `x in ]-oo, 0] uu [2, +oo [`

Explanation:

Let s factorise the expression

`4x^2-8x=4x(x-2)`

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

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

Now we can build the sign chart

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaaa)` `0` `color(white)(aaaaa)` `2` `color(white)(aaaa)` `+oo`

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

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

`color(white)(aaaa)` `f(x)` `color(white)(aaaaaa)` `+` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

Therefore,

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