Răspuns:
[tex](m+3)x^2-2(m-1)x+m-2=0; a=m+3;b=-2(m-1);c=m-2[/tex]
[tex]S=x1+x2=\frac{-b}{a}=\frac{2m-2}{m+3}[/tex]
[tex]P=x1x2=\frac{c}{a}=\frac{m-2}{m+3}[/tex]
[tex]2(x1+x2)-5x1x2=\frac{-2m+5}{2}[/tex]
[tex]2(\frac{2m-2}{m+3} )-5(\frac{m-2}{m+3})=\frac{-2m+5}{2}[/tex]
[tex]\frac{4m-4-5m+10}{m+3} =\frac{-2m+5}{2}[/tex]
[tex]\frac{-m+6}{m+3}=\frac{-2m+5}{2}[/tex]
[tex]2(-m+6)=(m+3)(-2m+5)[/tex]
[tex]-2m+12=-2m^2+5m-6m+15[/tex]
[tex]-2m^2+m+3=0[/tex]
[tex]-2m^2-2m+3m+3=0[/tex]
[tex]-2m(m+1)+3(m+1)=0[/tex]
[tex](-2m+3)(m+1)=0[/tex]
[tex]-2m+3=0=>m=\frac{3}{2}[/tex]
[tex]m+1=0=>m=-1[/tex]
