\(Δ=[-(2m-1)]^2-4.1.(-m+3)=4m^2-4m+1+4m-12=4m^2-11\\→Δ=4m^2-11<0\\↔(2m-\sqrt{11})(2m+\sqrt{11})\)
Pt vô nghiệm
\(→Δ=(2m-\sqrt{11})(2m+\sqrt{11})<0\\↔\left[\begin{array}{1}\begin{cases}2m-\sqrt{11}<0\\2m+\sqrt{11}>0\end{cases}\\\begin{cases}2m-\sqrt{11}>0\\2m+\sqrt{11}<0\end{cases}\end{array}\right.\\↔\left[\begin{array}{1}\begin{cases}m<\dfrac{\sqrt{11}}{2}\\m>-\dfrac{\sqrt{11}}{2}\end{cases}\\\begin{cases}m>\dfrac{\sqrt{11}}{2}\\m<-\dfrac{\sqrt{11}}{2}\end{cases}\end{array}\right.\\↔-\dfrac{\sqrt{11}}{2}<m<\dfrac{\sqrt{11}}{2}\)
Pt có 2 nghiệm phân biệt
\(→Δ=(2m-\sqrt{11})(2m+\sqrt{11})>0\\↔\left[\begin{array}{1}\begin{cases}2m-\sqrt{11}>0\\2m+\sqrt{11}>0\end{cases}\\\begin{cases}2m-\sqrt{11}<0\\2m+\sqrt{11}<0\end{cases}\end{array}\right.\\↔\left[\begin{array}{1}\begin{cases}m>\dfrac{\sqrt{11}}{2}\\m>-\dfrac{\sqrt{11}}{2}\end{cases}\\\begin{cases}m<\dfrac{\sqrt{11}}{2}\\m<-\dfrac{\sqrt{11}}{2}\end{cases}\end{array}\right.\\↔\left[\begin{array}{1}m>\dfrac{\sqrt{11}}{2}\\m<-\dfrac{\sqrt{11}}{2}\end{array}\right.\)
Pt có nghiệm kép
\(→Δ=(2m-\sqrt{11})(2m+\sqrt{11})=0\\↔\left[\begin{array}{1}2m-\sqrt{11}=0\\2m+\sqrt{11}=0\end{array}\right.\\↔\left[\begin{array}{1}m=\dfrac{\sqrt{11}}{2}\\m=-\dfrac{\sqrt{11}}{2}\end{array}\right.\)
