Ohio Department of Education
The Solution is Complex
Consider complex numbers, roots, and quadratic equations. Use the discriminate as a way to determine the nature of a quadratic's roots. Then discuss the similarities and differences between quadratics with two, one, or no real roots....
Curated OER
Complex Roots: A Graphical Solution
Using their Ti-Nspire to determine the solutions of parabolas, students explore the concept of complex roots. Students determine if parabolas have real or complex roots. Students determine the the axis of symmetry and the vertex given...
Curated OER
Who am I? Find A Polynomial From Its Roots
High schoolers generate the equation of a polynomial given its roots and the end behavior of the function. They need to apply theorems concerning the multiplicity of roots, conjugates of irrational or imaginary roots to find a...
Curated OER
Complex Roots Made Visible
For this algebra worksheet, 11th graders solve quadratic functions using the quadratic formula. They identify the negative roots using complex roots. There is an answer key with this problem.
Curated OER
Exploring Complex Roots
In exploring the concept of complex roots, students find the axis of symmetry and roots of parabolas. Then, they discuss what makes a solution complex and how to identify functions with complex roots.
Curated OER
Going Back to Your Roots
Investigate the Fundamental Theorem of Algebra and explore polynomial equations to determine the number of factors, the number of roots, and investigate multiplicity of roots.
Curated OER
Algebra II Test covering Radicals, Complex Numbers, and Finding Roots of Quadratics
In this algebra two worksheet, students solve twenty-five problems in test format. The worksheet covers radicals, complex numbers, and finding roots of quadratics.
EngageNY
Solving Quadratic Equations by Completing the Square
Many learners find completing the square the preferred approach to solving quadratic equations. Class members combine their skills of using square roots to solve quadratics and completing the square. The resource incorporates a variety...
Curated OER
Solving Quadratic Equations with Complex Roots
In this quadratic equations instructional activity, students solve 10 different equations that include complex roots. First, they solve for the indicated variable and express the roots of the equation in simplest form. Then, students...
Mathematics Vision Project
Quadratic Equations
Through a variety of physical and theoretical situations, learners are led through the development of some of the deepest concepts in high school mathematics. Complex numbers, the fundamental theorem of algebra and rational exponents...
EngageNY
An Appearance of Complex Numbers 1
Complex solutions are not always simple to find. In the fourth lesson of the unit, the class extends their understanding of complex numbers in order to solve and check the solutions to a rational equation presented in the first lesson....
EngageNY
Factoring Extended to the Complex Realm
A solution will work one way or another: find solutions, or use solutions to find the function. Learners use polynomial identities to factor polynomials with complex solutions. They then use solutions and the Zero Product Property to...
Alabama Learning Exchange
Complex Numbers Solutions
Complex doesn't have to mean harder! Learners experiment with online software to determine the quadratic equations with complex solutions. They use the quadratic formula to solve equations with both real and complex solutions.
Curated OER
The Discriminant
In this discriminant worksheet, 9th graders solve 10 different problems related to determining the discriminant in each equation. First, they find the nature of roots in quadratic equations. Then, students determine whether each of the...
Alabama Learning Exchange
Classifying Complex Numbers
Imaginary numbers are a real thing. Scholars learn about complex numbers, real numbers, and imaginary numbers. They classify given numbers as strictly complex, strictly real, or strictly imaginary in an individual or group activity.
Alabama Learning Exchange
As If Numbers Weren't Complex Enough Already!
The class explores the concept of complex numbers on a website to generate their own Mandelbrot sets. They will practice performing operations with complex numbers and then to get a visual understanding, graph the absolute value of a...
Inside Mathematics
Quadratic (2009)
Functions require an input in order to get an output, which explains why the answer always has at least two parts. After only three multi-part questions, the teacher can analyze pupils' strengths and weaknesses when it comes to quadratic...
Curated OER
The Quadratic Formula
In this Algebra II worksheet, 11th graders use the quadratic formula to solve quadratic equations and examine the discriminate to determine the number and type of roots a quadratic equation will have. The two page worksheet contains...
Curated OER
Imaginary and complex Numbers
For this Algebra II worksheet, 11th graders simplify expression involving imaginary and complex numbers and determine the quadratic equation that would have the given complex roots. The on page worksheet contains thirty-four problems. ...
Curated OER
Quadratics Equations
In this algebra worksheet, students define the equations and discuss how many and what kinds of roots there will be. There are 6 questions dealing with roots, complex numbers and quadratics.
Kuta Software
Imaginary Numbers
Here is a worksheet that takes all aspects of quadratic functions and incorporates imaginary numbers into the problems. The problems range from simplifying to graphing and solving by using a variety of methods with imaginary and complex...
EngageNY
End-of-Module Assessment Task - Algebra 2 (Module 1)
A series of assessment tasks require learners to process information and communicate solutions. Topics include graphing parabolas, solving linear-quadratic systems, factoring polynomials, and solving polynomial equations.
Curated OER
Standard Form
In this standard form instructional activity, 11th graders solve and complete 25 different types of problems. First, they write the value of each number given using standard form. Then, students add or multiply each given equation and...
Curated OER
Theorems About Roots and Polynomial Equations
In this algebra worksheet, students solve polynomial equations using factoring. They identify the roots of the equations. There are 3 questions with an answer key.