Proszę o pomoc.Równania wielomianowe.
1. x³+2x²-x-2=0
2.6x^4-12x³+6x²=0
3. x^4-3x³=3-x
1. x³+2x²-x-2=0x²(x+2)-(x+2)=0
(x²-1)(x+2)=0
x²-1=0
x²=1 ⇒ x₁=1; x₂=-1
x+2=0
x₃=-2
2.6x^4-12x³+6x²=06x²(x²-2x+1)=0
6x²=0 ⇒ x₁=0
x²-2x+1=0
Δ=4-4*1*1=4-4=0
x₂=2/2=1
x⁴-3x³+x-3=0
x(x³+1)-3(x³+1)=0
(x-3)(x³+1)=0
x-3=0 ⇒ x₁=3
x³+1=0
x³=-1 ⇒ x₂=-1
licze na naj
x²(x+2)-(x+2)=0
(x+2)(x²-1)=0
(x+2)(x-1)(x+1)=0
x+2=0 ∨x-1=0∨x+1=0
x₁=2∨x₂=1 ∨ x₃=-1
6x²(x²-2x+1)=0
6x²(x-1)²=0
x₁=0 ∨ x₂=1
x³(x-3)+(x-3)=0
(x³+1)(x-3)=0
(x+1)(x²-x+1)(x-3)=0
x₁=-1 ∨x₂=3
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1. x³+2x²-x-2=0
x²(x+2)-(x+2)=0
(x²-1)(x+2)=0
x²-1=0
x²=1 ⇒ x₁=1; x₂=-1
x+2=0
x₃=-2
2.6x^4-12x³+6x²=0
6x²(x²-2x+1)=0
6x²=0 ⇒ x₁=0
x²-2x+1=0
Δ=4-4*1*1=4-4=0
x₂=2/2=1
3. x^4-3x³=3-x
x⁴-3x³+x-3=0
x(x³+1)-3(x³+1)=0
(x-3)(x³+1)=0
x-3=0 ⇒ x₁=3
x³+1=0
x³=-1 ⇒ x₂=-1
licze na naj
1. x³+2x²-x-2=0
x²(x+2)-(x+2)=0
(x+2)(x²-1)=0
(x+2)(x-1)(x+1)=0
x+2=0 ∨x-1=0∨x+1=0
x₁=2∨x₂=1 ∨ x₃=-1
2.6x^4-12x³+6x²=0
6x²(x²-2x+1)=0
6x²(x-1)²=0
x₁=0 ∨ x₂=1
3. x^4-3x³=3-x
x⁴-3x³+x-3=0
x³(x-3)+(x-3)=0
(x³+1)(x-3)=0
(x+1)(x²-x+1)(x-3)=0
x₁=-1 ∨x₂=3