Odpowiedź:
Δ = [tex]b^{2}[/tex] - 4ac
a) Δ = [tex](-3)^{2}[/tex] - 4(2)(1) = 9 - 8 = 1
[tex]\sqrt{delta}[/tex] = 1
x1 = (-b - [tex]\sqrt{delta}[/tex])/2a = (3 - 1)/4 = 2/4 = [tex]\frac{1}{2}[/tex]
x2 = (-b + [tex]\sqrt{delta}[/tex] )/2a = (3 + 1)/4 = 4/4 = 1
x∈{[tex]\frac{1}{2}[/tex], 1}
b) Δ = 1 - 4(1)(-6) = 1 + 24 = 25
[tex]\sqrt{delta}[/tex] = 5
x1 = (1 - 5)/2 = -4/2 = -2
x2 = (1 + 5)/2 = 6/2 = 3
x∈{-2, 3}
c) Δ = 9 - 4(-1)(-2) = 9 - 8 = 1
[tex]\sqrt{delta}[/tex] = 1
x1 = (-3 - 1)/-2 = -4/-2 = 2
x2 = (-3 + 1)/-2 = -2/-2 = 1
x∈{1, 2}
d) Δ = 1 - 4([tex]\frac{1}{2}[/tex])(-[tex]\frac{3}{2}[/tex]) = 1 + 3 = 4
[tex]\sqrt{delta}[/tex] = 2
x1 = (-1 - 2)/1 = -3
x2 = (-1 + 2)/1 = 1
x∈{-3, 1}
e) Δ = 1 - 4(1)(-2) = 1 + 8 = 9
[tex]\sqrt{delta}[/tex] = 3
x1 = (1 - 3)/2 = -2/2 = -1
x2 = (1 + 3)/2 = 4/2 = 2
x∈{-1, 2}
