Odpowiedzi

2010-02-22T09:42:16+01:00
A) y=x²-9x+14
Δ=b²-4ac
Δ=81-56=25
√Δ=5
x₁=-b-√Δ/2a
x₂=-b+√Δ/2a
x₁=9-5/2=2
x₂=9+5/2=7
y=a(x-x₁)(x-x₂) <- postac iloczynowa
y=(x-2)(x-7)


b) y=x²-11x+18
Δ=121-72=49
√Δ=7
x₁=11-7/2=2
x₂=11+7/2=9
y=(x-2)(x-9)


c) 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)


d) y=-x²+8x+33
Δ=64+132=196
√Δ=14
x₁=-8-14/-2=-11
x₂=-8+14/-2=-3
y=-1(x+11)(x+3)


e) y=2x²+x-1
Δ=1+8=9
√Δ=3
x₁=-1-3/4=-1
x₂=-1+3/4=½
y=2(x+1)(x-½)


f) y=-2x²+5x+3
Δ=25+24=49
√Δ=7
x₁=-5-7/-4=3
x₂=-5+7/-4=-½
y=-2(x-3)(x+½)


g) y=-3x²-13x+10
Δ=169+120=289
√Δ=17
x₁=13-17/-6=⅔
x₂=13+17/-6=-5
y=-3(x-⅔)(x+5)


h) 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)


i) y=-6x²+x+2
Δ=1+48=49
√Δ=7
x₁=-1-7/-12=⅔
x₂=-1+7/-12=-½
y=-6(x-⅔)(x+½)


j) y=8x²+6x-9
Δ=36+288=324
√Δ=18
x₁=-6-18/16=-1½
x₂=-6+18/16=¾
y=8(x+1½)(x-¾)


k) y=-10x²+37-7
Δ=1369-280=1089
√Δ=33
x₁=-37-33/-20=3½
x₂=-37+33/-20=⅕
y=-10(x-3½)(x-⅕)