1. Rozwiąż równanie, nierówność kwadratową: a) 2x² - 3x = 9 b) x² - 9 ≤ 0 c) -2x² - 4x + 6 > 0 d) x³ + 5x² - 6 = 0 e) -2(x+1)(x-4) = 0 2. Rozwiąż algebraicznie i graficznie układ równań [latex] left { {{y=x+2} atop {y= x^{2} }} ight. [/latex]

[latex]1a) \\2x^2 - 3x = 9\2x^2 - 3x - 9=0 \ Delta =b^2-4ac =(-3)^2 -4*2* (- 9)= 9+72 = 81 \ \sqrt{Delta }=sqrt{81}=9 \ \x_{1}=frac{-b- sqrt{Delta } }{2a}=frac{3-9}{2 *2}=frac{-6}{4}= -frac{3}{2}\\x_{2}=frac{-b+ sqrt{Delta } }{2a}=frac{3+9}{2 *2}=frac{12}{4}= 3[/latex] [latex]d)\\ x^3+ 5x^2 - 6 = 0\x^3-x^2 +6x^2-6=0\x^2(x -1) +6(x^2-1)=0\x^2(x -1) +6(x -1)(x+1)=0\ (x -1 )(x^2+6 (x+1))=0\ (x -1) (x^2+6 x+6)=0\ x -1=0\ x=1\lub\ x^2+6 x+6 =0 \ Delta =b^2-4ac=6^2-4*1*6=36-24=12\\sqrt{Delta }=sqrt{12}= sqrt{4*3}=2sqrt{3} \ \x_{1}=frac{-b- sqrt{Delta } }{2a}=frac{-6-2sqrt{3}}{2 }= frac{2(-3- sqrt{3})}{2 }= -3- sqrt{3} \ \x_{2}=frac{-b+sqrt{Delta } }{2a}=frac{-6+2sqrt{3}}{2 }= frac{2( sqrt{3}-3)}{2 }= sqrt{3}-3\rozwiazanie:\x=1 vee [/latex] [latex]e)\\ -2(x+1)(x-4) = 0\\x+1=0 vee x-4=0\\x=-1 vee x=4[/latex] [latex]2)\\egin{cases}y=x+1 \ y=x^2 end{cases}\\egin{cases} x^2=x+2 \ y=x^2 end{cases} \\egin{cases} x^2-x-2=0\ y=x^2 end{cases} \\ x^2-x-2=0\\Delta =b^2-4ac = (-1)^2 -4*1* (-2)= 1+8 = 9\\sqrt{Delta }=sqrt{9}=3 \ \x_{1}=frac{-b- sqrt{Delta } }{2a}=frac{1- 3}{2 }=frac{-2}{2}=-1 \\x_{2}=frac{-b+ sqrt{Delta } }{2a}=frac{1+ 3}{2 }=frac{4}{2} =2[/latex] [latex]egin{cases}x= -1 \ y=x^2 end{cases} vee egin{cases}x= 2 \ y=x^2 end{cases}\\ egin{cases}x= -1 \ y= (-1)^2 end{cases} vee egin{cases}x= 2 \ y= (2)^2 end{cases}\\egin{cases}x= -1 \ y=1 end{cases} vee egin{cases}x= 2 \ y= 4 end{cases}[/latex]