<s>[INST] Find $a$ if $(a+3)x^2-4x+2<0$ $\forall x\in [-2,1]$ Find $a$ if $(a+3)x^2-4x+2<0 \qquad \forall x\in [-2,1]$
My Attempt:
$a+3=0$ $\implies -4x+2<0$
$$2x-1>0$$
$$x>\dfrac {1}{2}$$
$\implies a \neq -3$.
 [/INST] Let $f(x)=(a+3)x^2-4x+2$
1) Let $a+3>0 \Leftrightarrow a>-3$. 
Then $f(-2)<0$ and $f(1)<0$

$f(-2)<0 \Leftrightarrow 4(a+3)+10<0$, then $a<-\frac{11}{2}$
$f(-1)<0 \Leftrightarrow a+3-2<0$, then $a<-1$
2) Let $a+3>0$ and let $x_0=\frac{4}{2(a+3)}$
Then $f(-2)<0$ and $f(1)<0$ and $x_0\not\in[-2;1]$
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