Cześć!
a)
[tex]x^2-x-6=0\\\\a=1, \ b=-1, \ c=-6\\\\\Delta=(-1)^2-4\cdot1\cdot(-6)=1+24=25\\\\\sqrt{\Delta}=\sqrt{25}=5\\\\x_1=\frac{-(-1)-5}{2\cdot1}=\frac{1-5}{2}=\frac{-4}{2}=-2\\\\x_2=\frac{-(-1)+5}{2\cdot1}=\frac{1+5}{2}=\frac{6}{2}=3[/tex]
b)
[tex]3x^2+4x+1=0\\\\a=3, \ b=4, \ c=1\\\\\Delta=4^2-4\cdot3\cdot1=16-12=4\\\\\sqrt{\Delta}=\sqrt4=2\\\\x_1=\frac{-4-2}{2\cdot3}=\frac{-6}{6}=-1\\\\x_2=\frac{-4+2}{2\cdot3}=\frac{-2}{6}=-\frac{1}{3}[/tex]
c)
[tex]4x^2-7x-2=0\\\\a=4, \ b=-7, \ c=-2\\\\\Delta=(-7)^2-4\cdot4\cdot(-2)=49+32=81\\\\\sqrt{\Delta}=\sqrt{81}=9\\\\x_1=\frac{-(-7)-9}{2\cdot4}=\frac{7-9}{8}=-\frac{2}{8}=-\frac{1}{4}\\\\x_2=\frac{-(-7)+9}{2\cdot4}=\frac{7+9}{8}=\frac{16}{8}=2[/tex]
Wykorzystane wzory
[tex]y=ax^2+bx+c\\\\\Delta=b^2-4ac\\\\x_1=\frac{-b-\sqrt{\Delta}}{2a} \ oraz \ x_2=\frac{-b+\sqrt{\Delta}}{2a} \ (gdy \ \Delta>0)[/tex]
