Question

How do you solve `x^2-3x-4>=0` using a sign chart?

Answer 1

The answer is `-oo < x <=-1` and `4<= x<+oo`

Explanation:

Start by factorising
`x^2-3x-4=(x+1)(x-4)`
let `y=(x+1)(x-4)`
So we can make the sign chart
`x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-1` `color(white)(aaaa)` `4` `color(white)(aaaa)` `+oo`
`x+1` `color(white)(aaaa)` `-` `color(white)(aaaaa)` `+` `color(white)(aaaa)` `+`
`x-4` `color(white)(aaaa)` `-` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `+`
`y` `color(white)(aaaaaaaa)` `+` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `+`

So `x^2-3x-4>=0`
when `-oo < x <=-1` and when `4<= x<+oo`