Question

How do you solve `x^2+x-6>0`?

Answer 1

The answer is `x in ] -oo,-3[ uu ] 2, oo[`

Explanation:

We start by factorising the expression

`x^2+x-6=(x-2)(x+3)`

and

let `f(x)=(x-2)(x+3)`

Now, we can make the sign chart

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-3` `color(white)(aaaaa)` `2` `color(white)(aaaa)` `+oo`

`color(white)(aaaa)` `x+3` `color(white)(aaaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+`

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

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

Therefore,

`f(x)>0`, when `x in ] -oo,-3[ uu ] 2, oo[`