[tex]zad.1\\\\-x^{2} -6x-9 <0~~\mid \div (-1)\\\\x^{2} +6x+9>0\\\\a=1,~~b=6,~~c=9\\\\\Delta=b^{2} -4ac\\\\\Delta=36^{2} -4\cdot 1\cdot 9 = 36-36=0\\\\\Delta = 0~~\Rightarrow ~~funkcja~~kwadratowa ~~posiada~~jeden ~~pierwiastek~~x_{0} =\dfrac{-b}{2a} \\\\x_{0} =\dfrac{-6}{2\cdot 1} =-3\\\\x^{2} +6x+9>0~~\land~~x_{0} =-3~~\land~~a=1~(a>0~~ramiona~~paraboli~~skierowane ~~do~~gory)\\\\x^{2} +6x+9>0 ~~\Rightarrow ~~x\in R - \{ -3 \}[/tex]
[tex]zad.2\\\\(4x+2)\cdot (x-5) < (2x+1)\cdot (x-7)\\\\4x^{2} -20x+2x-10<2x^{2} -14x+x-7\\\\4x^{2} -18x-10<2x^{2} -13x-7\\\\4x^{2} -2x^{2} -18x+13x-10+7<0\\\\2x^{2} -5x-3<0\\\\a=2,~~b=-5,~~c=-3\\\\\Delta = x^{2} -4ac\\\\\Delta = (-5)^{2} -4\cdot 2\cdot (-3)=25+24=49=7^{2} \\\\\sqrt{\Delta} =7\\\\x_{1} =\dfrac{-b-\sqrt{\Delta} }{2a} ~~\lor~~x_{1} =\dfrac{-b+\sqrt{\Delta} }{2a}\\\\\\x_{1} =\dfrac{5-7}{4} ~~\lor ~~x_{2} =\dfrac{5+7}{4}\\\\x_{1}=-\dfrac{1}{2} ~~\lor~~x_{2} =3\\\\[/tex]
[tex]2x^{2} -5x-3<0~~\land ~~ (x_{1} =-\dfrac{1}{2} ~~\lor~~x_{2} =3)~~\land ~~a=2 ~~(a>0~~ramona ~~paraboli~~skierowane ~~do ~~gory)\\\\2x^{2} -5x-3<0~~\Rightarrow ~~x\in (-\dfrac{1}{2} ,3)[/tex]
