Know the Fundamental Theorem of Algebra and connect it to polynomial roots.
Determine the total number of complex roots of a polynomial from its degree
Problem
How many complex roots does this polynomial have in total: \(\text{degree}~4\) polynomial?
Big Picture
What this problem is really about
The Fundamental Theorem of Algebra connects a polynomial's degree directly to its total number of complex roots. That total counts repeated roots according to multiplicity and includes real roots because the real numbers sit inside the complex numbers. The number of distinct roots can be smaller, but the sum of their multiplicities still equals the degree.
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.
