Question

How do you solve `x^2+6x-16>0` using a sign chart?

Answer 1

The answer is `x in ] -oo,-8 [ uu ]2, +oo[`

Explanation:

Let's factorise the expression

`x^2+6x-16=(x+8)(x-2)`

and let `f(x)=(x+8)(x-2)`

Now we can do the sign chart

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-8` `color(white)(aaaa)` `2` `color(white)(aaaa)` `+oo`

`color(white)(aaaa)` `x+8` `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,-8 [ uu ]2, +oo[`