Show that all roots of the eq. (z + 1)^3 + z^3 = 0 lie on the line

x = -1/2

thank you.

Printable View

- Apr 14th 2006, 07:29 PMunicorna complex numbers problem
Show that all roots of the eq. (z + 1)^3 + z^3 = 0 lie on the line

x = -1/2

thank you. - Apr 15th 2006, 01:24 AMCaptainBlackQuote:

Originally Posted by**unicorn**

lie on then should be a real root.

This checks out, so we know that is a factor of the cubic,

and so we use long division to find the remaining quadratic factor:

Now we can use that quadratic formula to verify that the two remaining

roots (which are the roots of ) have real parts

(which they do).

RonL - Apr 16th 2006, 02:51 PMunicorn
thanks :)