Mathematics - Quadratic Equation Question with Solution | TestHub

The discriminant $D$ must be positive for real and distinct roots. $D=(-(m+1){)}^2-4(1)(m^2-3m+4)>0$. This simplifies to $m^2+2m+1-4m^2+12m-16>0⟹-3m^2+14m-15>0⟹3m^2-14m+15<0$. Factoring the quadratic, we get $(3m-5)(m-3)<0$. Thus, $5/3<m<3$. The only integer $m$ in this interval is $2$. Hence, there is $1$ integral value.