Question

How do you solve `4x^2-9x+2<0`?

Answer 1

The answer is `1/4 < x < 2`

Explanation:

Let's factorise the expression `f(x=)4x^2-9x+2=(4x-1)(x-2)`
`(4x-1)(x-2)<0`
We make a sign chart to solve the problems
`color(white)(aaaaaa)` `x` `color(white)(aaa)` `-oo` `color(white)(aaa)` `1/4` `color(white)(aaa)` `2` `color(white)(aaa)` `+oo`
`color(white)(aaaa)` `4x-1` `color(white)(aaaa)` `-` `color(white)(a)` `0` `color(white)(a)` `+` `color(white)(aaa)` `+`
`color(white)(aaaaa)` `x-2` `color(white)(aaaa)` `-` `color(white)(aaa)` `-` `color(white)(a)` `0` `color(white)(a)` `+`
`color(white)(aaaaa)` `f(x)` `color(white)(aaaaa)` `+` `color(white)(aaa)` `-` `color(white)(a)` `0` `color(white)(a)` `+`

So `f(x<0)` when `1/4 < x < 2`
graph{(4x-1)(x-2) [-7.024, 7.024, -3.51, 3.513]}