Wyznacz pierwiastki wielomianu W(x)=9x3-x2-27x+3
W(x) = 9x³-x²-27x+3 = 9x³-27x-x²+3 = 9x(x²-3)-(x²-3) = (9x-1)(x²-3) =(9x-1)(x+√3)(x-√3)
W(x) = 0
(9x-1)(x+√3)(x-√3) = 0
9x-1 = 0 => x = 1/9
lub
x+√3 = 0 => x = -√3
x-√3 = 0 => x = √3
Odp. x = -√3 v x = 1/9 v x = √3
W(x)=9x^3-x^2-27x+3
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W(x) = 9x³-x²-27x+3 = 9x³-27x-x²+3 = 9x(x²-3)-(x²-3) = (9x-1)(x²-3) =(9x-1)(x+√3)(x-√3)
W(x) = 0
(9x-1)(x+√3)(x-√3) = 0
9x-1 = 0 => x = 1/9
lub
x+√3 = 0 => x = -√3
lub
x-√3 = 0 => x = √3
Odp. x = -√3 v x = 1/9 v x = √3
W(x)=9x^3-x^2-27x+3