# Complex numbers (roots of equations) help

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• Nov 12th 2012, 10:40 AM
ineedmathshelp
Complex numbers (roots of equations) help
Using that 3 is the real root of the cubic equation x^3-27=0, show that the complex roots of the cubic satisfy the quadratic equation x^2+3x+9=0.

hence or otherwise find the three cube roots of 27 giving your answers in the form a+ib

thankyou!
• Nov 12th 2012, 10:50 AM
Plato
Re: Complex numbers (roots of equations) help
Quote:

Originally Posted by ineedmathshelp
Using that 3 is the real root of the cubic equation x^3-27=0, show that the complex roots of the cubic satisfy the quadratic equation x^2+3x+9=0. hence or otherwise find the three cube roots of 27 giving your answers in the form a+ib

Given that $3$ is root of $x^3-27=0$ means that $(x-3)$
is a factor. So $(x-3)(?)=x^3-27$.