range of values and conditions

• Mar 28th 2013, 10:57 PM
Renrie
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!
Attachment 27729
• Mar 29th 2013, 04:54 AM
Ruun
Re: range of values and conditions
You are given a polynomial of degree two in \$\displaystyle x\$, \$\displaystyle x^2-3x-10\$. A convenient way of writing it is in the form \$\displaystyle (x-x_1)(x-x_2)\$ where \$\displaystyle x_1\$ and \$\displaystyle 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 \$\displaystyle x_1,x_2\$ set a change of sign in the expression \$\displaystyle x^2-3x-10\$. So you should check whether is positive or negative if \$\displaystyle x\$ is greater or smaller than \$\displaystyle x_1\$ and \$\displaystyle x_2\$.

Also for the absolute value condiction \$\displaystyle |x-2|<a\$ this means \$\displaystyle -a<x-2<a\$
• Mar 29th 2013, 06:53 AM
HallsofIvy
Re: range of values and conditions
Essentially, you are asked to solve an inequality: \$\displaystyle x^2- 3x- 10< 0\$. And the simplest way to do that is to solve the associated equation. As Ruun suggests, we can factor \$\displaystyle 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".