p(x)=x^4-6x^2+3x+2
p(1)=1-6+3+2 = 0
x= 1 is root
let p(x) = (x-1)(x^3+bx^2+cx+d)
compare the coef.of constant
-d = 2 => d =-2
compare the coef.of x^3
-1+b = 0
b = 1
compare the coef of x
-c+ d = 3
-c-2 =3
c = -5
p(x)=(x-1)(x^3+x^2-5x-2)
p(2)=0
x=2 is root
let
(x^3+x^2-5x-2) = (x-2)(x^2+ex+f)
compare the coef.of constant
-2f=-2
f=1
compare the coef of x^2
e-2 =1
e = 3
(x^3+x^2-5x-2) = (x-2)(x^2+3x+1)
p(x)=(x-1)(x-2)(x^2+3x+1)
x^2+3x+1 = 0
x = (-3+√5) / 2 or (-3-√5) / 2
零点:1,2,(-3+√5) / 2 ,(-3-√5) / 2
附加：p(1）=0,这不是固定的解法,这只适合这个方程而已. p(x)=x^4-6x^2+3x+2
p(1)=1-6+3+2 = 0
x= 1 is root
let p(x) = (x-1)(x^3+bx^2+cx+d)
compare the coef.of constant
-d = 2 => d =-2
compare the coef.of x^3
-1+b = 0
b = 1
compare the coef of x
-c+ d = 3
-c-2 =3
c = -5
p(x)=(x-1)(x^3+x^2-5x-2)
p(2)=0
x=2 is root
let
(x^3+x^2-5x-2) = (x-2)(x^2+ex+f)
compare the coef.of constant
-2f=-2
f=1
compare the coef of x^2
e-2 =1
e = 3
(x^3+x^2-5x-2) = (x-2)(x^2+3x+1)
p(x)=(x-1)(x-2)(x^2+3x+1)
x^2+3x+1 = 0
x = (-3+√5) / 2 or (-3-√5) / 2
零点:1,2,(-3+√5) / 2 ,(-3-√5) / 2
附加：p(1）=0,这不是固定的解法,这只适合这个方程而已.