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

User Barnaby
by
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1 Answer

6 votes
Hello,

1)

x^(4)-3x^(3)-6x^(2)+8x=x(x^3-3x^2-6x+8)


=x(x^(3)-x^(2)-2x^2+2x-8x+8)=x(x^(2)(x-1)-2x(x-1)-8(x-1))


=x(x-1)(x^2-2x-8)=x(x-1)(x^2+2x-4x-8)


=x(x-1)(x(x+2)-4(x+2))=x(x-1)(x+2)(x-4)


2)


x^(3)+10x^(2)+169x=x(x^2+10x+169)=x(x+5-12i)(x+5+12i)


User Amit Meena
by
8.1k points

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