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2010-02-20T18:29:45+01:00
A)x²- 5x -14=0
Δ=81
√Δ=9
x₁=5-9/2*1
x₁=-4/2
x₁=-2

x₂=5+9/2
x₂=14/2
x₂=7
postac iloczynowa y= (x+2)(x-7)

b)x²+8x+33=0
Δ=-68 rozwiazanie w postaci iloczynowej nie istnieje

c)2x²+5x+3=0
Δ=1
√Δ=1
x₁=-5 -1/2*2
x₁=-6/4
x₁=-3/2

x₂=-5 +1/4
x₂=-4/4
x₂=-1
postac iloczynowa y=(x+3/2)(x+1)

d)3x²-13x+10=0
Δ=49
√Δ=7
x₁=13-7/2*3
x₁=6/6
x₁=1

x₂=13+7/6
x₂=20/6
x₂=10/3
postac iloczynowa y=(x-1)(x-10/3)

e)3x²-x-4
Δ=49
√Δ=7
x₁=1-7/2*3
x₁=-6/6
x₁=-1

x₂=1+7/6
x₂=8/6
x₂=4/3
postac iloczynowa y=(x+1)(x-4/3)

f)-6x²+x+2=0
Δ=49
√Δ=7
x₁=-1-7/-12
x₁=-6/-12
x₁=1/6

x₂=-1+7/-12
x₂=6/-12
x₂=-1/6
postac iloczynowa y=(x-1/6)(x+1/6)

g)8x²+6x-9=0
Δ=324
√Δ=18
x₁=-6-18/2*8
x₁=-24/16
x₁=3/2

x₂=-6+18/16
x₂=12/16
x₂=3/4
postac iloczynowa y=(x-3/2)(x-3/4)

h)-10x²+37x-7=0
Δ=1089
√Δ=33
x₁=-37-33/-20
x₁=-70/-20
x₁=7/2

x₂=-37+33/-20
x₂=-4/-20
x₂=1/5
postac iloczynowa y=(x-7/2)(x-1/5)
2010-02-20T18:53:34+01:00
A) y=x²-5x-14
Δ=25+56=81
√Δ=9
x₁=5-9/2=-2
x₂=5+9/2=7
y=(x+2)(x-7)
b) y=x²+8x+33
Δ=64-132=-68
nie ma postaci iloczynowej,brak miejsc zerowych
c) y=2x²+5x+3
Δ=25-24=1
√Δ=1
x₁=-5-1/4=-6/4=-1½
x₂=-5+1/4=-1
y=2(x+1½)(x+1)
d) y=3x²-13x+10
Δ=169-120=49
√Δ=7
x₁=13-7/6=1
x₂=13+7/6=3⅓
y=3(x-1)(x-3⅓)
e) y=3x²-x-4
Δ=1+48=49
√Δ=7
x₁=1-7/6=-1
x₂=1+7/6=1⅓
y=3(x+1)(x-1⅓)
f) y=-6x²+x+2
Δ=1+48=49
√Δ=7
x₁=-1-7/-12=8/12=⅔
x₂=-1+7/-12=-½
y=-6(x-⅔)(x+½)
g) y=8x²+6x-9
Δ=36+288=324
√Δ=18
x₁=-6-18/16=-24/16=-1½
x₂=-6+18/16=12/16=¾
y=8(x+1½)(x-¾)
h) y=-10x²+37x-7
Δ=1369-280=1089
√Δ=33
x₁=-37-33/-20=7/2=3½
x₂=-37+33/-20=-5/-20=¼
y=-10(x-3½)(x-¼)

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