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Math Help - make up a polynomial

  1. #1
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    make up a polynomial

    make up a polynomial that has the following characteristics: crosses the x axis at -1 and 4 , touches the a-axis at 0 and 2 and is above the a axis between 0 and 2.
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by alessandromangione View Post
    make up a polynomial that has the following characteristics: crosses the x axis at \color{red}-1 and \color{red}4 , touches the a-axis at \color{blue}0 and \color{blue}2 and is above the a axis between \color{green}0 and \color{green}2.
    What do you mean by the a-axis? If this is just a typo (and a recurring one at that), then

    p(x)={\color{green}c}\cdot {\color{red}(x+1)(x-4)}{\color{blue}x^2(x-2)^2}

    will do. In order to have p(x) > 0 for x\in ]0;2[ you need to make c<0.
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