x^8+17x^6+88x^4+144x^2=0 想問這麼求解 答案是0.0.+-2埃.+-2埃.+-3埃?

Sol
x^3+17x^2+88x+144
=(x^3+8x^2+16x)+(9x^2+72x+144)
=x(x^2+8x+16)+9(x^2+8x=16)
=(x+9)(x^2+8x+16)
x^8+17x^6+88x^4+144x^2
=x^2(x^6+17x^4+88x^2+144)
=x^2(x^2+9)(x^4+8x^2+16)
=x^2(x^2+9)(x^2+4)^2
x=0(重根) or x=2i(重根) or x=－2i(重根) or x=+/-3i