Hej!
a]
[tex]4x^2-5x=0\\\\4x(x-1,25)=0\\\\4x=0\rightarrow x=0\\\\x-1,25=0\rightarrow x=1,25[/tex]
b]
[tex]x^2-4x-5=0\\\\a=1, \ b=-4, \ c=-5\\\\\Delta=(-4)^2-4\cdot1\cdot(-5)=16+20=36\\\\\sqrt{\Delta}=\sqrt{36}=6\\\\x_1=\frac{-(-4)-6}{2\cdot1}=\frac{4-6}{2}=\frac{-2}{2}=-1\\\\x_2=\frac{-(-4)+6}{2\cdot1}=\frac{4+6}{2}=\frac{10}{2}=5[/tex]
c]
[tex]x^2+x-1\geq0\\\\a=1, \ b=1, \ c=-1\\\\\Delta=1^2-4\cdot1\cdot(-1)=1+4=5\\\\\sqrt{\Delta}=\sqrt5\\\\x_1=\frac{-1-\sqrt5}{2}\\\\x_2=\frac{-1+\sqrt5}{2}\\\\x\in(-\infty;\frac{-1-\sqrt5}{2}\rangle\cup\langle\frac{-1+\sqrt5}{2};+\infty)[/tex]
Ramiona paraboli skierowane do góry, kółeczka zamalowane
