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Math Help - Polynomial inequality

  1. #1
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    Polynomial inequality

    Solve the poynomial inequality. Write the answer in interval notation. Could you show your work since I don't get these. Thanks
    (T-7)(T+1) is less than 0.

    x^3 + 36 is greater than to 4x^2 + 9x
    Last edited by rowdy3; April 30th 2008 at 06:17 AM. Reason: wrong number
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  2. #2
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    Hello,

    Quote Originally Posted by rowdy3 View Post
    Solve the poynomial inequality. Write the answer in interval notation. Could you show your work since I don't get these. Thanks
    (T-7)(T+1) is less than 0.
    A product is negative if the two factors are of different sign.

    -> T-7>0 and T+1<0
    Or T-7<0 and T+1>0

    x^3 + 36 is greater than to 4x^2 + 9x
    For this one,

    x^3+36>4x^2+9x

    <=> (x^3-9x)+(36-4x^2)>0

    <=> x(x-9)+4(9-x)>0

    <=> (x-9)(x-4)>0


    A product is positive if its factors are of the same sign.

    -> x-9>0 and x-4>0
    Or x-9<0 and x-4<0
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    x^2 + 2x + 1 less than 0
    This is what I did.
    X^2 + 2x + 1 less than 0.
    -1 -1
    x^2 + 2x less than -1
    Divide by x.
    x + 2 less than -1
    No solution.
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    Quote Originally Posted by rowdy3 View Post
    x^2 + 2x + 1 less than 0
    This is what I did.
    X^2 + 2x + 1 less than 0.
    -1 -1
    x^2 + 2x less than -1
    Divide by x.
    x + 2 less than -1
    No solution.
    Hehe, don't bother ^^

    x+2x+1=(x+1)

    Can a squared number be negative ?
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    Ouuuh, I missed a mistake :

    Divide by x.
    x + 2 less than -1
    Do you know why, in my first post, I only said that there were two solutions ?
    Because you don't know if x is positive or negative.

    If it's positive, it keeps the sign of the inequality.
    If it's negative, < will become >.

    An example :

    6>4
    If you divide both sides by -2, is it -3>-2 or -3<-2 ?

    Be careful about this
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