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Professor Dave Explains
Linear Second-Order Differential Equations Part 1: Homogeneous Case
After a number of tutorials covering first-order differential equations, it's time to start tackling second-order differential equations. These contain a second derivative term, and they are quite useful in physics. To introduce these,...
Curated Video
Finding Zeros of Polynomials Using Graphing Calculators
In this video, the teacher explains how to find the zeros of a polynomial function using a graphing calculator. They demonstrate the process of long division to determine factors and use the quadratic formula to solve quadratic...
Brian McLogan
Solving a quadratic equation with imaginary solutions
👉Learn how to solve quadratic equations by factoring when a is equal to 1. A quadratic is an algebraic expression having 2 as the highest power of its variable(s). To factor an algebraic expression means to break it up into factors...
Brian McLogan
Learn how to solve using quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a...
Brian McLogan
Using the discriminate to describe the number and type of solutions
👉 Learn how to solve a quadratic equation by applying the quadratic formula. To apply the quadratic formula the quadratic equation must be equal to zero. Then you can apply the quadratic formula to determine solutions to the equation,...
Brian McLogan
How to use the quadratic formula to solve a quadratic equation
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a...
Curated Video
Graphing Quadratic Functions and Understanding Complex Roots
In this video, the teacher explains the graphical meaning of real and complex roots in quadratic functions. They review function notation and the steps to graph a quadratic function. They also explain how to use the discriminant to...
Curated Video
Identifying Real and Complex Roots of Quadratic Equations
In this video, the teacher explains how to identify whether a quadratic equation has real or complex roots without actually solving it. The concept of the discriminant is introduced and its role in determining the number and type of...
Brian McLogan
Determine the number of positive, negative and complex roots of a polynomial
👉 Learn about Descartes' Rule of Signs. Descartes' rule of the sign is used to determine the number of positive and negative real zeros of a polynomial function. Knowing the number of positive and negative real zeros enables also to also...
Brian McLogan
Given the imaginary zeros find the equation of the polynomial
👉 Learn how to write the equation of a polynomial when given imaginary zeros. Recall that a polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The...
Flipped Math
Imaginary Numbers
Leave nothing to the imagination! Learners view a thorough lesson on imaginary numbers that introduces the concept, shows how to simplify square roots of negative numbers, and then how to solve quadratic equations with imaginary...
Welch Labs
Imaginary Numbers Are Real (Part 8: Math Wizardry)
How does the Fundamental Theorem of Algebra apply to equations with complex roots? Using recently learned concepts about the complex plane, learners determine all the complex roots of polynomials. They can find the same roots...
Pearson
Using the Fundamental Theorem of Algebra
Here's help in making the giant leap from finding real to finding complex roots. Careful and thorough in explanation, the theory of polynomial algebra is briefly touched upon before the examples really dive into the application...
Krista King Math
Completing the Square with Complex Roots
Explore completing the square as a process for finding complex roots of quadratic equations with a video lesson that pulls together several concepts related to quadratic equations. The example shows how to complete the square with a...
Curated OER
How Do You Solve a Quadratic Equation with Complex Solutions by Completing the Square?
The quadratic equation x2,3,4x + 5 = 0 is solved by completing the square in this video. Two complex solutions are found and are checked in the original equation to verify that they are solutions.
Khan Academy
Khan Academy: Pre Calculus: Exponential Form to Find Complex Roots
This video illustrates how the exponential form of a complex number can be helpful in finding the complex roots of a number. The process is shown both algebraically and graphically using x^3 = 1 as a simple example. [11:53]
Khan Academy
Khan Academy: Pre Calculus: Complex Determinant Example
A video showing the step-by-step solution to a difficult determinant problem from the IIT-JEE. This is problem 53 from Paper 1 of the 2010 exam. A 3 X 3 matrix is given in terms of z and omega, where omega is defined as a complex number...
Khan Academy
Khan Academy: Complex Roots of the Characteristic Equations 2
What happens when the characteristic equation has complex roots?
Khan Academy
Khan Academy: Repeated Roots of the Characteristic Equation
What happens when the characteristic equation only has 1 repeated root?
Khan Academy
Khan Academy: Complex Roots of the Characteristic Equations 3
Complex and repeated roots of characteristic equation.
Khan Academy
Khan Academy: Repeated Roots of the Characteristic Equations Part 2
An example where we use initial conditions to solve a repeated-roots differential equation.