Question

How do you solve `x^2-3x>=10` using a sign chart?

Answer 1

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

Explanation:

Let's rewrite the equation

`x^2-3x-10>=0`

Let `f(x)=x^2-3x-10=(x+2)(x-5)`

The domain of `f(x)` is `D_f(x)=RR`

Let's do the sign chart

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

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

`color(white)(aaaa)` `x-5` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

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

So,

`f(x)>=0` when `x in ] -oo,-2 ] uu [5, +oo[`