Extend polynomial identities to complex numbers for higher-degree polynomial work.
List complex roots as repeated multiplicity records
Problem
For \((x~-~i)^{2}(x~+~i)\), list every root with multiplicity, give the total degree, and determine whether the conjugate multiplicities are consistent with all-real coefficients.
Big Picture
What this problem is really about
Read each root from a factor of the form x minus r, and read its multiplicity from that factor's exponent. Add the multiplicities to recover the polynomial's degree rather than counting only distinct root values. If the expanded coefficients are claimed to be real, every nonreal root must occur with its conjugate at the same multiplicity.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
