8.求函数f(x)=x3-2x2-x+2的零点要有详细过程

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8.求函数f(x)=x3-2x2-x+2的零点要有详细过程
8.求函数f(x)=x3-2x2-x+2的零点
要有详细过程

8.求函数f(x)=x3-2x2-x+2的零点要有详细过程
f(x) = x³-2x²-x+2 = x³-x-(2x²-2)
= x(x²-1)-2(x²-1)
= (x-2)(x²-1)
= (x-2)(x-1)(x+1)
零点
2,1,-1

X³-2X²-X+2=0
X²(X-2)-(X-2)=0
(X²-1)(X-2)=0
X=±1,X=2

f(x)=x3-x2-(x2-x+2)
=x2(x-1)-(x-2)(x-1)
=(x2-x+2)(x-1)
=(x+1)(x-2)(x-1)
零点是-1,1,2