Mathematics - Quadratic Equation Question with Solution | TestHub

For real and distinct roots, the discriminant $D$ must be greater than zero. Here, $D=(-(m+1){)}^2-4(1)(m^2-3m+3)=m^2+2m+1-4m^2+12m-12=-3m^2+14m-11$. Setting $D>0$ gives $-3m^2+14m-11>0$, which simplifies to $3m^2-14m+11<0$. Factoring the quadratic, we get $(3m-11)(m-1)<0$, which implies $1<m<\frac{11}{3}$.