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Rozłóż na czynniki :
3x⁴-7x³+7x-3
3x⁴-7x³+7x-3 = 3(x⁴-1)-7(x³-x)= 3(x²-1)(x²+1) - 7x(x²-1) =(x²-1) [3(x²+1)-7x] = (x²-1) (3x²-7x+3) = (x-1)(x+1)(3x²-7x+3) = 3(x-1)(x+1)(x -(7+√13)/6 ) (x- (7-√13)/6)
Δ=49 - 36= 13
x₁=(7+√13)/6
x₂=(7-√13)/6
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3x⁴-7x³+7x-3 = 3(x⁴-1)-7(x³-x)= 3(x²-1)(x²+1) - 7x(x²-1) =(x²-1) [3(x²+1)-7x] = (x²-1) (3x²-7x+3) = (x-1)(x+1)(3x²-7x+3) = 3(x-1)(x+1)(x -(7+√13)/6 ) (x- (7-√13)/6)
Δ=49 - 36= 13
x₁=(7+√13)/6
x₂=(7-√13)/6