[tex]a)\\\\ x^2+2x-3=0\\\\a=1,\ \ b=2\ \ c=-3\\\\\Delta=b^2-4ac=2^2-4*1*(-3)=4+12=16\\\\\sqrt{\Delta }=\sqrt{16}=4\\\\x_{1} = \frac{-b-\sqrt{\Delta }}{2a}=\frac{-2-4}{2*1}=\frac{-6}{2}=-3\\\\x_{2} = \frac{-b+\sqrt{\Delta }}{2a}=\frac{-2+4}{2*1}=\frac{2}{2}=1[/tex]
[tex]b)\\\\ x^2+2x+1=0\\\\a=1,\ \ b=2\ \ c=1\\\\\Delta=b^2-4ac=2^2-4*1*1=4-4=0\\\\ x_{0} = \frac{-b }{2a}=\frac{-2 }{2*1}=\frac{-2}{2}=-1[/tex]
[tex]c)\\\\ 2x^2-x+8=0\\\\a=2,\ \ b=-1\ \ c=8\\\\\Delta=b^2-4ac= (-1)^2-4*2*8=1-64=-63\\\\ \Delta <0,\ \ brak \ pierwiastkow[/tex]
[tex]d)\\\\ x^2-4=0\\\\ (x-2)(x+2)=0\\\\x-2=0\ \ lub\ \ x+2=0\\\\x=2\ \ lub\ \ x=-2[/tex]
[tex]e)\\\\ 2x^2-10=0\\\\ 2(x^2-5)=0\\\\2(x- \sqrt{5})(x+ \sqrt{5})=0\\\\x-\sqrt{5} =0\ \ lub\ \ x+ \sqrt{5}=0\\\\x= \sqrt{5}\ \ lub\ \ x=- \sqrt{5}[/tex]
[tex]f)\\\\ 2x^2 +27=x^2+18\\\\x^2-x^2=18-27\\\\0=-9\\\\rownanie\ sprzeczne,\ brak\ rozwiazania[/tex]
