Oblicz:
a)xkwadrat+2x+1=0
b)xkwadrat-4x=0
c)2xkwadrat+x+4=0
d)xkwadrat-5x+6=0
e)xkwadrat-9=0
f)2xkwadrat+x+2=0
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a)
delta = 4 - 4 = 0
x = -b/2a
x = -2/2
x = -1
b)
delta = 16
Pierw. z delty = 4
x1 = 4 -4/2 = 0
x2= 4 +4 / 2 = 8/2 = 4
c) delta = 1 - 4*2*4 = 1 - 32 = -31
delta < 0
brak miejsc zerowych
d) delta = 25 - 4*1*6 = 25 - 24 = 1
pierw. z delty = 1
x1= 5 - 1 / 2 = 4/2 = 2
x2 = 5 +1 / 2 = 6/2 = 3
e) x kwadrat - 9 = 0
x kwadrat = 9
x = 3 lub x = -3
f) delta = 1 - 4 * 2 * 2 = 1 - 16 = - 15
delta < 0
brak rozwiązań
a)
delta= (2 do kwadratu)- 4*1*1= 0
x1= -2/2 =-1
b) (-4kwadrat) - 4*1=12
delta=pierwiastek z 12
pierwiastek z delty =2pierw z 3
x1= 4+ 2pierwz3/ 2*1 = 4+2pierw z 3/ 2
x2= 4-2pierwz3 p/ 2*1 = 4-2pierw z 3/2
c) delta = (1 do kwadratu) - 4*4*(-2) = 33
pierwiastek z delty =pierw z 33
x1=1+pierwz33/ 2*2=1+pierwz33 / 4
x2=1-pierwz33 / 2*2=1-pierwz33/ 4
d) (-5 do kwadratu) - 4*6 = 25-24 = 1
x1= 5+1/2*1 = 3
x2=5-1/2 =2
e) (-9dokwadratu) - 4*1= 81-4=77
pierw z delty=pierw z 77
x1= 1+pirwz77/ 2
x2= 1-pierwz77/2
f) 1dokwadratu - 4*2*2= - 17 delta nei ma rozwiazania