a)
y=2x^2-14x+20
\Delta=b^2-4ac=(-14)^2-4*2*20=196-160=36
\sqrt{\Delta}=\sqrt{36}=6
x_1=\frac{-b-\sqrt{\Delta}}{2a}=\frac{14-6}{4}=2
x_2= \frac{-b+\sqrt{\Delta}}{2a}=\frac{14+6}{4}=5
b)
y=-\frac{1}{3}x^2+\frac{4}{3}x-\frac{4}{3}
-\frac{1}{3}x^2+\frac{4}{3}x-\frac{4}{3}=0/*(-3)
x^2-4x+4=0
wzór (a-b)^2=a^2-2ab+b^2
(x-2)^2=0
x-2=0
pierwiastek dwukrotny x=2
c)
y=6x^2+x
6x^2+x=0
x(6x+1)=0
x_1=0 lub 6x+1=0
6x=-1/:6
x_2=-\frac{1}{6}
Odp. x_1=0, x_2=-\frac{1}{6}
d)
y=-15x^2+3
-15x^2+3=0/:(-15)
x^2-\frac{1}{5}=0
(x-\sqrt{\frac{1}{5}})(x+\sqrt{\frac{1}{5}})=0
x-\sqrt{\frac{1}{5}}=0 lub x+\sqrt{\frac{1}{5}}=0
x_1=\frac{1}{\sqrt5}*\frac{\sqrt5}{\sqrt5}=\frac{\sqrt5}{5}
Podobnie z minusem
x_2=-\frac{\sqrt5}{5}