2. Polynomials and Rational

Polynomial Roots — Quiz

Test your understanding of polynomial roots with 5 practice questions.

Practice Questions

Question 1

Given a polynomial $P(x)$ with real coefficients, if $3 - 4i$ is a root, which of the following must also be a root?

Question 2

A polynomial function has a graph that touches the x-axis at $x = 2$ and crosses the x-axis at $x = -1$. Which of the following could be the polynomial?

Question 3

Consider the polynomial $P(x) = x^3 - 5x^2 + 11x - 15$. Given that $x = 3$ is a root, find the other roots.

Question 4

A polynomial $P(x)$ with real coefficients has roots $1, 2, 4i. What is the minimum possible degree of $P(x)$?

Question 5

If a polynomial $P(x)$ has a root $x = -2$ with multiplicity $3$ and a root $x = 1 - i$, what is the minimum degree of $P(x)$?