Question
If $f(x)$ is a polynomial of degree $n \geq 1$ with complex coefficients, then $f(x)$ has exactly _____ complex zeros, provided that each zero is counted by its multiplicity.
Step 1
A polynomial of degree $n$ is a polynomial whose highest power of the variable is $n$. For example, $f(x) = x^3 + 2x^2 + x + 1$ is a polynomial of degree 3. Show more…
Show all steps
Your feedback will help us improve your experience
James Kiss and 78 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros: -3+3i; -1 multiplicity 2 Let a represent the leading coefficient. The polynomial is f(x) = a(x + 3 - 3i)(x + 3 + 3i)(x + 1)(x + 1)
A complex polynomial function f of degree 4 with real coefficients has the zeros - 1, 2, and 3 - i. Find the remaining zero(s) of f. Then find a polynomial function that has the zeros.
If $f(x)$ is a polynomial of degree $n \geq 1$ with complex coefficients, then $f(x)$ has at least one complex zero. This is the statement of what important theorem?
Polynomial and Rational Functions
Zeros of Polynomials
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD