Odpowiedź:
[tex]a)\\\\-2x^2-8x+10=0\ \ /:(-2)\\\\x^2+4x-5=0\\\\\Delta=b^2-4ac=4^2-4*1*(-5)=16+20=36\\\\\sqrt{\Delta}=\sqrt{36}=6\\\\\\x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-4-6}{2*1}=\frac{-10}{2}=-5\\\\\\x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-4+6}{2*1}=\frac{2}{2}=1[/tex]
[tex]b)\\\\3x^2+2x-1=0\\\\\Delta=b^2-4ac=2^2-4*3*(-1)=4+12=16\\\\\sqrt{\Delta}=\sqrt{16}=4\\\\\\x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-2-4}{2*3}=\frac{-6}{6}=-1\\\\\\x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-2+4}{2*3}=\frac{2}{6}=\frac{1}{3}[/tex]
[tex]c)\\\\-\frac{1}{2}x^2-4x-8=0\ \ /*2\\\\-x^2-8x-16=0\\\\\Delta=b^2-4ac=(-8)^2-4*(-1)*(-16)=64-64=0\\\\\sqrt{\Delta}=0\\\\\\x_{0}=\frac{-b}{2a}=\frac{-(-8)}{2*(-1)}=\frac{8}{-2}=-4[/tex]
[tex]d)\\\\x^2+2x+6=0\\\\\Delta=b^2-4ac=2^2-4*1*6=4-24=-20\\\\\Delta<0\ \ r\'ownanie\ \ nie\ \ ma\ \ rozwiazania[/tex]
