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Math Help - Inequality

  1. #1
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    Inequality

    Guys please help i have like a whole exercise on these can someone please provide a working answear.

    x^3+5x^2+2x-8/x^3-7x^2+7x+15<=0 <= means less then or equal to
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  2. #2
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    Re: Inequality

    Quote Originally Posted by iFuuZe View Post
    Guys please help i have like a whole exercise on these can someone please provide a working answear.

    x^3+5x^2+2x-8/x^3-7x^2+7x+15<=0 <= means less then or equal to
    You need to use brackets where they're needed so we can understand what the inequation actually is.

    Is it \displaystyle \begin{align*} \frac{x^3 + 5x^2 + 2x - 8}{x^3 - 7x^2 + 7x + 15} \leq 0 \end{align*}?
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  3. #3
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    Re: Inequality

    Quote Originally Posted by iFuuZe View Post
    Guys please help i have like a whole exercise on these can someone please provide a working answear.

    x^3+5x^2+2x-8/x^3-7x^2+7x+15<=0 <= means less then or equal to
    Inequality is equivalent to the :

    \frac{(x-1)(x+4)(x+2)}{(x-5)(x-3)(x+1)} \leq 0
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  4. #4
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    Re: Inequality

    yep so you factorice the top and bottom now what we do procede....
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    Re: Inequality

    Quote Originally Posted by iFuuZe View Post
    yep so you factorice the top and bottom now what we do procede....
    A function will only ever stop being negative at the x intercepts, so evaluate where they are, then test some points between each of them to determine which of the regions give negative values for the function
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    Re: Inequality

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    Re: Inequality

    Quote Originally Posted by Prove It View Post
    A function will only ever stop being negative at the x intercepts...
    or at a discontinuity.
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    Re: Inequality

    Quote Originally Posted by a tutor View Post
    or at a discontinuity.
    Let's assume we've already established that \displaystyle \begin{align*} x \neq -1, 3, 5 \end{align*} :P
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    Re: Inequality

    Quote Originally Posted by Prove It View Post
    Let's assume we've already established that \displaystyle \begin{align*} x \neq -1, 3, 5 \end{align*} :P
    Of course.

    I'm just pointing out that you can get a sign change at a discontinuity too.
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  10. #10
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    Re: Inequality

    guys i dont understand, its better if i visualise a worked example if any can do that it would fantastic
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  11. #11
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    Re: Inequality

    Sign changes occur whenever the sign of one factor changes.

    This will happen at x= -4,-2,-1,1,3 and 5.

    So check x<-4. Here all factors <0 so the expression is positive.

    x<-4 positive
    -4<x<-2 negative
    -2<x<-1 positive
    -1<x<1 negative
    1<x<3 positive
    3<x<5 negative
    x>5 positive
    Thanks from iFuuZe
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