Question

How do you solve `(x+5)(x-2)>=0`?

Answer 1

The answer is `x in ] -oo,-5 ] uu [2, +oo[`

Explanation:

Let `f(x)=(x+5)(x-2)`

Now, we can do a sign chart

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-5` `color(white)(aaaa)` `2` `color(white)(aaaa)` `+oo`

`color(white)(aaaa)` `x+5` `color(white)(aaaaa)` `-` `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,-5 ] uu [2, +oo[`

graph{(x+5)(x-2) [-28.86, 28.85, -14.43, 14.43]}