x^4-5x^2+10x+24=0

x^4-5x^2+4 + 10x+20 = 0
(x^2-1)(x^2-4)+10(x+2)=0
(x+2)(x^3-x-2x^2+2+10)=0
(x+2)(x^3-2x^2-x+12)=0
所以有一个解x=-2
x^3-2x^2-x+12不能再分解了,可以用三次方程求根公式得到精确解
他的解分别为
x1=1/3 (2 - 7/(145 - 3 Sqrt[2298])^(1/3) - (145 - 3 Sqrt[2298])^(1/3)) = -1.88968
x2=2/3 + (7 (1 + I Sqrt[3]))/(6 (145 - 3 Sqrt[2298])^(1/3)) +
1/6 (1 - I Sqrt[3]) (145 - 3 Sqrt[2298])^(1/3)
= 1.94484 + 1.60245 i
x3=2/3 + (7 (1 - I Sqrt[3]))/(6 (145 - 3 Sqrt[2298])^(1/3)) +
1/6 (1 + I Sqrt[3]) (145 - 3 Sqrt[2298])^(1/3)
=1.94484 - 1.60245 i

x^4-5x^2+10x+24=0
x^4+2x^3-2x^3-4x^2-x^2-2x+12x+24=0
x^3(x+2)-2x^2(x+2)-x(x+2)+12(x+2)=0
(x+2)(x^3-2x^2-x+12)=0
x+2=0,x^3-2x^2-x+12=0
x=-2