I'm trying to find the conditions on $a, b$, and $c$ so that a $2$nd-degree polynomial satisfies the following inequality when $x$ is in $[0,1]:$
$0 < c + bx + ax^2 < 1$
I found the following requirements:
$ 0 < c < 1;$
$0 < a + b + c < 1;$
But this is not enough. Any help would be gold!