$a,b,c \in \mathbb{R}$ and for all $-1<x<1$
Show that if $|ax^2+bx+c|=<1$
So :
1) $|c|=<1$
2) $|a+c|=<1$
3) $a^2+b^2+c^2=<5$
For the first one ; if I choose x=0
So |c|=<1
And choosing $x=1$ and $x=-1$ give us |a+b|=<1
So did I prove it for all $x \in [-1,1]$ ?
If No then how can I show it ?
Can someone give me a hint for the third one ?