Hệ pt vô nghiệm $⇔Δ<0$
$⇔Δ=b²-4ac=[-2(m-1)]²-4.(m+2).4<0$
$⇔4(m-1)²-16(m+2)<0$
$⇔4(m²-2m+1)-16m-32<0$
$⇔4m²-8m+4-16m-32<0$
$⇔4m²-24m-28<0$
$⇔m²-6m-7<0$
$⇔m²+m-7m-7<0$
$⇔m(m+1)-7(m+1)<0$
$⇔(m+1)(m-7)<0$
$⇔$ \(\left[ \begin{array}{l}m+1<0\\m-7<0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}m<-1\\m<7\end{array} \right.\)