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Math Help - [SOLVED] Sign of a Quadratic

  1. #1
    Brian D
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    [SOLVED] Sign of a Quadratic

    Solve : x^2 - 4x + 3 < 0


    I need to graph the solution also
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  2. #2
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    Quote Originally Posted by Brian D
    Solve : x^2 - 4x + 3 < 0


    I need to graph the solution also
    (1) Factorize
    x^2 - 4x + 3 = (x-3)*(x-1)

    (2) Think, when is (x-3)*(x-1) negative (less than zero)? When each parenthetical group has a different sign.

    Possibilities:
    (a) x<3 making (x-3) negative AND x>1 making (x-1) positive
    (b) x>3 making (x-3) positive AND x<1 making (x-1) negative

    Therefore, 1<x<3

    On a number line, open circles at 1 and 3 and connect them.
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  3. #3
    MHF Contributor

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    The simplest way to solve "complicated" inequalities is to solve the EQUATION. Where something is EQUAL to 0 separates where it is positive from where it is negative! (If your inequality involves fractions, you want to check points where the denominator is 0 also.)

    x^2- 4x+ 3= (x- 3)(x- 1)= 0 when x= 3 or x= 1.

    Now check a value in each of the three intervals x< 1, 1< x< 3, 3< x.

    0 is less than 1 and 0^2- 4(0)+ 3= 3 which is positive.

    2 is between 1 and 3 and 2^2- 4(2)+ 3= 4- 8+ 3= -1 which is negative

    4 is larger than 3 and 4^2- 4(4)+ 3= 16- 16+ 3= 3 which is positive.

    We now know that x^2- 4x+ 3 is negative for ALL numbers between 1 and 3 and negative for ALL numbers less than 1 or larger than 3.
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  4. #4
    MHF Contributor
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    To HallsofIvy

    You are wrong!

    "...and negative for ALL numbers less than 1 or larger than 3."
    Yeah?
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  5. #5
    Site Founder MathMan's Avatar
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    Quote Originally Posted by ticbol
    You are wrong!

    "...and negative for ALL numbers less than 1 or larger than 3."
    Yeah?
    Lets try and keep this place civil...
    We all make mistakes
    Last edited by MathMan; April 21st 2005 at 10:17 AM.
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  6. #6
    MHF Contributor
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    To MathMan

    I did not start it.

    HallsofIvy blew in here like he could tell me something.
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