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Thread: 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 $\displaystyle \color{red}-1$ and $\displaystyle \color{red}4$ , touches the a-axis at $\displaystyle \color{blue}0$ and $\displaystyle \color{blue}2$ and is above the a axis between $\displaystyle \color{green}0$ and $\displaystyle \color{green}2$.
    What do you mean by the a-axis? If this is just a typo (and a recurring one at that), then

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

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