Câu 4:
Để $f(x)\ge 0\quad\forall x\in\mathbb{R}, \Delta'\le 0$
$\Delta'=(m+2)^2-(-m^2-3m-1)$
$=m^2+4m+4+m^2+3m+1$
$=2m^2+7m+5$
$=(m+1)(2m+5)\le 0$
$\to \dfrac{-5}{2}\le m\le -1$
Câu 5:
$\Delta ABC$ có $c=2, b=5, A=120^o$
$\to S_{ABC}=\dfrac{1}{2}bc\sin A=\dfrac{1}{2}.2.5\sin120^o=\dfrac{5\sqrt3}{2}$
$BC=a=\sqrt{b^2+c^2-2bc\cos A}=\sqrt{39}$