# Thread: range of values and conditions

1. ## range of values and conditions

here the answer would be basically:

i) AB: 2<x<1
ii) C: 6
iii) D: 8

could you please explain to me how to solve it and understand it properly? Thanks!

2. ## Re: range of values and conditions

You are given a polynomial of degree two in $x$, $x^2-3x-10$. A convenient way of writing it is in the form $(x-x_1)(x-x_2)$ where $x_1$ and $x_2$ are its roots, this is, the numbers such that the polynomial is zero.

Now the reasoning: Because the polynomial is a continuous function, these two numbers $x_1,x_2$ set a change of sign in the expression $x^2-3x-10$. So you should check whether is positive or negative if $x$ is greater or smaller than $x_1$ and $x_2$.

Also for the absolute value condiction $|x-2| this means $-a

3. ## Re: range of values and conditions

Essentially, you are asked to solve an inequality: $x^2- 3x- 10< 0$. And the simplest way to do that is to solve the associated equation. As Ruun suggests, we can factor $x^2- 3x- 10= (x- 5)(x+ 2)= 0$. So where is that equal to 0? Those points separate "> 0" from "< 0". Just pick one value in each interval to see whether it is "> 0" or "< 0".