Question

If the equaiton $a{x}^2+bx+c=0(a>0)$ has two real roots $\alpha$ and $\beta$ such that $\alpha$ $<-2$ and $\beta$ $>2$ then $a+|b|+c<m$.Find $m$

Answer 1

Two real roots ; $b^2-4ac>0$
$\alpha$$<-2$ ; $\beta$ $>2$
$\alpha$ $<0<$ $\beta$ $\Rightarrow$ $f\left(0\right)=c<0$
$f(-1)=a-b+c<0$
$f\left(1\right)=a+b+c<0$
$\Rightarrow$ $a+|b|+c<0$.

Therefore $m=0$