Question

How do you solve `x^2+x-6<0` using a sign chart?

Answer 1

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

Explanation:

Let's factorise the expression,

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

and let `f(x)=x^2+x-6`

Now we can do 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)(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 ] -3,2 [`