Rozłóż wielomian na czynniki:
b) 3x⁴-5x³+5x²-5x+2
3x⁴-5x³+5x²-5x+2=
=3x⁴-5x³+2x²+3x²-5x+2=
=x²(3x²-5x+2)+1(3x²-5x+2)=
=(x²+1)(3x²-5x+2)=
=(x²+1)(x - 2/3)(x-1)
3x²-5x+2=0
Δ=b²-4ac=25-24=1
√Δ=1
x₁=[-b-√Δ]/2a=2/3
x₂=[-b-√Δ]/2a=1
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3x⁴-5x³+5x²-5x+2=
=3x⁴-5x³+2x²+3x²-5x+2=
=x²(3x²-5x+2)+1(3x²-5x+2)=
=(x²+1)(3x²-5x+2)=
=(x²+1)(x - 2/3)(x-1)
3x²-5x+2=0
Δ=b²-4ac=25-24=1
√Δ=1
x₁=[-b-√Δ]/2a=2/3
x₂=[-b-√Δ]/2a=1