[tex]a)\\x(x^2-(2m-4)x+m-2)=0\\x=0\\\\x^2-(2m-4)x+m-2=0\\a=1\\b=-(2m-4)=-2m+4=4-2m\\c=m-2\\\\\Delta=0\\(4-2m)^2-4*1*(m-2)=0\\16-16m+4m^2-4m+8=0\\4m^2-20m+24=0\\\\\Delta_2=(-20)^2-4*4*24=400-384=16\\\sqrt{\Delta_2}=4\\[/tex]
[tex]m_1=\frac{20-4}{8}=\frac{16}8=2\\m_2=\frac{20+4}8=3\\\\\text{Dla }m=2\\\Delta=4*2^2-20*2+24=4*4-40+24=0\\b=4-2*2=0\\c=2-2=0\\x_0=\frac{0}2=0\\\\\text{Dla m=3}\\\Delta=4*3^2-20*3+24=4*9-60+24=36-36=0\\b=4-2*3=4-6=-2\\c=3-2=1\\x_0=\frac{2}{2}=1\\\\\text{Dla m=2 rownanie ma jedno rozwiazanie: x=0}\\\text{Dla m=3 rownanie ma 2 rozwiazania: x=0, x=1}\\\\\text{Odp. Rownanie ma jedno rozwiazanie dla parametru m=2}[/tex]
[tex]b) \\(x+3)(x^2+(m+3)x+m^2)=0\\x+3=0\\x=-3\\\\x^2+(m+3)x+m^2=0\\a=1\\b=m+3\\c=m^2\\\\\Delta=0\\(m+3)^2-4*1*m^2=0\\m^2+6m+9-4m^2=0\\-3m^2+6m+9=0\\\\\Delta_2=6^2-4*(-3)*9=36+108=144\\\sqrt{\Delta_2}=12\\m_1=\frac{-6-12}{{-6}}=\frac{-18}{-6}=3\\m_2=\frac{-6+12}{-6}=\frac{6}{-6}=-1[/tex]
[tex]\text{Dla m=3:}\\\Delta=-3*3^2+6*3+9=-3*9+18+9=-27+27=0\\a=1\\b=3+3=6\\c=3^2=9\\x_1=\frac{-6}2=-3[/tex]
[tex]\text{Dla m=-1}\\\Delta=-3*(-1)^2+6*(-1)+9=-3-6+9=-9+9=0\\a=1\\b=-1+3=2\\c=(-1)^2=1\\x_0=\frac{-2}2=-1[/tex]
[tex]\text{Dla paramteru m=3, rownanie ma jedno rozwiazanie: x=-3}\\\text{Dla paramteru m=-1, rownanie ma dwa rozwiazania: x=-3, x=-1}\\\\\text{Odp. Rownanie ma jedno rozwiazanie dla parametru m=3}[/tex]