leansantilla
leansantilla leansantilla
  • 13-07-2016
  • Mathematics
contestada

Find all possible complex roots of x^4-3x^3-6x^2+8x and of x^3+10x^2+169x

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caylus
caylus caylus
  • 13-07-2016
Hello,

1)
[tex] x^{4}-3x^{3}-6x^{2}+8x=x(x^3-3x^2-6x+8)[/tex]

[tex] =x(x^{3}-x^{2}-2x^2+2x-8x+8)=x(x^{2}(x-1)-2x(x-1)-8(x-1))[/tex]

[tex] =x(x-1)(x^2-2x-8)=x(x-1)(x^2+2x-4x-8)[/tex]

[tex] =x(x-1)(x(x+2)-4(x+2))=x(x-1)(x+2)(x-4)[/tex]


2)

[tex]x^{3}+10x^{2}+169x=x(x^2+10x+169)=x(x+5-12i)(x+5+12i) [/tex]


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