Odpowiedź:
[tex]a)\\\\x^2+6x-7=0\\\\a=1\ \ ,\ \ b=6\ \ ,\ \ c=-7\\\\\Delta=b^2-4ac\\\\\Delta=6^2-4\cdot1\cdot(-7)=36+28=64\\\\\sqrt{\Delta}=\sqrt{64}=8\\\\\\x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-6-8}{2\cdot1}=\frac{-14}{2}=-7\\\\x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-6+8}{2\cdot1}=\frac{2}{2}=1[/tex]
[tex]b)\\\\x^2+2x+1=0\\\\a=1\ \ ,\ \ b=2\ \ ,\ \ c=1\\\\\Delta=b^2-4ac\\\\\Delta=2^2-4\cdot1\cdot1=4-4=0\\\\\sqrt{\Delta}=\sqrt{0}=0\\\\\\x_{0}=-\frac{b}{2a}=-\frac{2}{2\cdot1}=-\frac{2}{2}=-1\\\\\\lub\\\\x^2+2x+1=0\\\\(x+1)^2=0\\\\x+1=0\\\\x=-1[/tex]
[tex]c)\\\\-x^2-4x-3=0\\\\a=-1\ \ ,\ \ b=-4\ \ ,\ \ c=-3\\\\\Delta=b^2-4ac\\\\\Delta=(-4)^2-4\cdot(-1)\cdot(-3)=16-12=4\\\\\sqrt{\Delta}=\sqrt{4}=2\\\\\\x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2}{2\cdot(-1)}=\frac{4-2}{-2}=\frac{2}{-2}=-1\\\\\\x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2\cdot(-1)}=\frac{4+2}{-2}=\frac{6}{-2}=-3[/tex]
