2. Polynomial Analysis

Complex Polynomials — Quiz

Test your understanding of complex polynomials with 5 practice questions.

Practice Questions

Question 1

A real-coefficient cubic polynomial has roots 1 and 2+3i. What is its third root?

Question 2

Which monic quartic polynomial has roots $i,\;-i,\;2,\;\text{and}\;-3$?

Question 3

Which quadratic factor corresponds to roots $5\pm i$ in a real-coefficient polynomial?

Question 4

Given the cubic $P(x)=x^3-3x^2+5x-m$ has a root $1+2i$, what is $m$?

Question 5

How many nonreal roots does a degree-7 polynomial with real coefficients have if it has exactly three real roots?