Question

How do you solve `x^2+21>10x` using a sign chart?

Answer 1

The answer is `x in ] -oo,3 [ uu ] 7, +oo[`

Explanation:

Let's rearrange the equation

`x^2-10x+21>0`

Let `f(x)=x^2-10x+21`

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

Let's factorise

`f(x)=(x-3)(x-7)`

Now, we can establish the sign chart

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `3` `color(white)(aaaaa)` `7` `color(white)(aaaa)` `+oo`

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

`color(white)(aaaa)` `x-7` `color(white)(aaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+`

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

Therefore,

`f(x)>0` when `x in ] -oo,3 [ uu ] 7, +oo[`