Thread: a 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.

Originally Posted by unicorn

Show that all roots of the eq. (z + 1)^3 + z^3 = 0 lie on the line
x = -1/2
thank you.

First observe that a cubic has at least one real root. So if all the roots
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

thanks