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Math Help - range of values and conditions

  1. #1
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    Wink 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!
    range of values and conditions-gfddg.jpg
    Last edited by Renrie; March 28th 2013 at 10:59 PM.
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  2. #2
    Member Ruun's Avatar
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    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|<a this means -a<x-2<a
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  3. #3
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    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".
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