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Math Help - Hi i need help with poynomial inequalities

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    Hi i need help with poynomial inequalities

    Hi there I am working thru this problem and my solution is (neg infinity, 3/2) Here is the problem : 2x^3-7x^2<-6x

    My textbook has a different answer of x>3/2 am I wrong or is the book wrong?
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    Re: Hi i need help with poynomial inequalities

    I get:

    (-\infty,0)\,\cup\,\left(\frac{3}{2},2 \right)
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    Re: Hi i need help with poynomial inequalities

    Quote Originally Posted by shannan55 View Post
    Hi there I am working thru this problem and my solution is (neg infinity, 3/2) Here is the problem : 2x^3-7x^2<-6x

    My textbook has a different answer of x>3/2 am I wrong or is the book wrong?
    I think that you are both mistaken.

    If you factor you get

    2x^3-7x^2+6x < 0 \iff x(x-2)\left(2x-3 \right)< 0

    This gives

     \begin{tabular}{|c|c|c|c|c|} \hline  f(x) & - &+ &- &+ \\ \hline x & - & + & + & + \\ \hline (2x-3) & - & -& + & + \\ \hline (x-2) & - & - & - & + \\ \hline  & (infinity,0) & (0,3/2) & ( 3/2, 2 ) & (2, infinity) \\ \hline \end{tabular}

    So the solution should be

    (-\infty,0) \cup \left( \frac{3}{2},2\right)
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