x^3-5x^2+5x+5=0

问题描述:

x^3-5x^2+5x+5=0

∴ x³-5x² 5x 5
X^3-5X^2 5X 5
=X(X^2-5X 5) 5
=X[(X^2-3X-1) (-2X 6)] 5
=X(X^2-3X-1) X(-2X 6) 5
=X(X^2-3X-1)-2(X^2-3X-1) 3.
=(x-2)(x^2-3x-1) 3=0
∴x1=1,
【注:若一个多项式各项系数和为0,则该多项式必然含有因式x-1
若一个多项式奇数项系数之和等于偶数项系数,则该多项式必然含有因式x 1】

x^3-5x^2 5x 5=0这是个一元三次方程,用盛金公式得三个根:x1=(5-(100^(1/3) 10^(1/3))/3x2=(5 sin30°[100^(1/3) 10^(1/3)] cos30°[100^(1/3)-10^(1/3)]i)/3x3=(5 sin30°[100^(1/3) 10^(1/3)]-cos30°[100^(1/3)-1...