Zadanie 2
-x^2+6x-9=0
-(x^2-6x+9)=0/*(-1)
x^2-6x+9=0
(x-3)^2=0
x-3=0
x=3 pierwiastek dwukrotny
b)
-3x^2+8x-11=0
a=-3, b=8, c=11
\Delta=b^2-4ac=64-4*(-3)*11=64+132=196
\sqrt\Delta=14
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-8-14}{2*(-3)}=\frac{-22}{-6}=-\frac{11}{3}=-3\frac{2}{3}
x_2=\frac{-b-\sqrt\Delta}{2a}=\frac{-8+14}{-6}=1
c)
7x^2-12x+5=0
7x^2-7x-5x+5=0
7x(x-1)-5(x-1)=0
(x-1)(7x-5)=0
x-1=0\vee 7x-5=0
x=1\vee x=\frac{5}{7}
d)
3x^2-2x+1=0
a=3, b=-2, c=1 , a>0 ramiona paraboli skierowane w górę
\Delta=4-4*3*1=-8
\Delta<0 brak pierwiastków
x\in \mathbb R
http://www.wolframalpha.com/input/?i=3x^2-2x%2B1%3D0
e)
-4x^2+3x-\frac{9}{16}=0/*(-16)
64x^2-48x+9=0
a=64, b=-48, c=9
\Delta=2304-4*64*9-2304=0
x_0=-\frac{b}{2a}=-\frac{\not48^6}{2*\not64^8}=-\frac{6}{16}=-\frac{3}{8}