Question

How do you solve `x^4-13x^2+36<=0`?

Answer 1

The answer is `-3<=x<=-2` and `2<=x<=3`

Explanation:

Let's start by factorising the expression
`x^4-13x^2+36=(x^2-4)(x^2-9)`
`=(x-2)(x+2)(x-3)(x+3)`

So `(x-2)(x+2)(x-3)(x+3)<=0`
Let's do a sign chart
`x` `color(white)(aaaaaaaaaaa)` `-3` `color(white)(aaaa)` `-2` `color(white)(aaaa)` `2` `color(white)(aaaa)` `3`
`x+3` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+` `color(white)(aaa)` `+`
`x+2` `color(white)(aaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaaa)` `+` `color(white)(aaa)` `+`
`x-2` `color(white)(aaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaa)` `+`
`x-3` `color(white)(aaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaa)` `+`