# Math Help - make up a polynomial

1. ## 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.

2. Originally Posted by alessandromangione
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 $c<0$.