[tex]a)\\\\postac\ iloczynowa\ funkcji\ kwadratowej:\\\\y=a(x-x_{1})(x-x_{2})\\\\y=x^2+3x+2\\\\a=1,\ \ b=3,\ \ c=2\\\\\Delta =b^2-4ac=3^2-4*1*2=9-8=1\\\\\sqrt{\Delta }=\sqrt{1}=1 \\\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{-3-1 }{2*1}=\frac{-4}{2}=-2 \\\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{-3+1 }{2*1}=\frac{-2}{2}=-1\\\\y=(x-(-2))(x-(-1))=(x+2)(x+1)[/tex]
[tex]b)\\\\ y=2x^2-2x-40\\\\a=2,\ \ b=-2,\ \ c=-40 \\\\\Delta =b^2-4ac= (-2)^2-4*2* (-40)= 4+320=324\\\\\sqrt{\Delta }=\sqrt{324}= 18 \\\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{2-18 }{2*2 }=\frac{-16}{4}=-4 \\\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{2+18 }{2*2}=\frac{20}{4}=5\\\\y=2(x-(-4))(x- 5)=2(x+4)(x-5)[/tex]
