Solving Quadratic Equations with Imaginary Solutions

The Organic Chemistry Tutor

This video tutorial provides a step-by-step guide on solving quadratic equations that result in imaginary (complex) solutions. The instructor demonstrates two different types of problems: simple binomial equations that can be solved by isolating the variable and taking square roots, and trinomial equations that require the quadratic formula because they cannot be factored using integers. The core concept reinforced throughout is the definition of the imaginary unit $i$, where the square root of -1 equals $i$. The lesson explores key algebraic themes including the properties of square roots, the manipulation of negative radicands, and the application of the quadratic formula. It specifically addresses how to handle a negative discriminant (the value under the square root in the quadratic formula) and how to properly format the final complex answer in the standard form $a \pm bi$. The distinction between factorable and non-factorable quadratics is also highlighted as a decision-making step in the problem-solving process. For educators, this video serves as an excellent resource for Algebra 2 or Pre-Calculus units on complex numbers. It offers clear, procedural modeling that helps students transition from real-number solutions to the complex number system. The video can be used to introduce the concept of imaginary roots, reinforce the mechanics of the quadratic formula, or support students who struggle with simplifying radicals containing negative numbers.