D - delta, pD - pierwiastek z delty
A) (x + 3)(x + 1) = -1
x^2 + x + 3x + 3 + 1 = 0
x^2 + 4x + 4 = 0
D = b^2 - 4ac = 4^2 - 4*1*4 = 16 - 16 = 0 <gdy D=0 jest jedno miejsce zerowe)
x0 = (-b)/2a = (-4)/2 = -2
B) (x + 4)^2 - 8x = 2
x^2 + 2*x*4 + 4^2 - 8x - 2 = 0
x^2 + 8x + 16 - 8x - 2 = 0
x^2 + 14 = 0
D = b^2 - 4ac = 0^2 - 4*1*14 < 0 (gdy D<0 nie ma miejsc zerowych)
C) (1 - 3x)^2 = 1 - 6x
(-3x)^2 + 2*1*(-3x) + 1^2 - 1 + 6x = 0
9x^2 - 6x + 1 - 1 + 6x = 0
9x^2 = 0
x^2 = 0
D = b^2 - 4ac = 0^2 - 4*1*0 = 0 - 0 = 0
x0 = (-b)/2a = 0/2 = 0
D) x + 9 = (x - 3)^2
x + 9 = x^2 - 2*x*3 + 3^2
x + 9 = x^2 - 6x + 9
x^2 - 6x + 9 - x - 9 = 0
x^2 - 7x = 0
D = b^2 - 4ac = (-7)^2 - 4*1*0 = 49 (kiedy D>0 są dwa miejsca zerowe)
pD = 7
x1 = (-b - pD)/2a = (-(-7) - 7)/2 = (7 - 7)/2 = 0
x2 = (-b + pD)/2a = (-(-7) + 7)/2 = (7 + 7)/2 = 14/2 = 7