Solving Quadratic Equations: What is the Most Efficient Method?

Solving Quadratic Equations: What is the Most Efficient Method?

Because there are several techniques for solving quadratic equations, a preliminary analysis is useful to determine the method that minimizes both arithmetic and algebraic calculations. We have carefully crafted our own preliminary analysis. We call the method selected by our analysis the Most Efficient Method.

Often, there is one method that stands out as the most efficient method; at other times, it can be a matter of hairsplitting to decide between two methods that are roughly equal in effort. We checked exercises in over 10 algebra, college algebra, and precalculus textbooks, and our preliminary analysis worked precisely as we wanted for those problems. We encourage you to do your own preliminary analysis.

Of course, even experts can disagree about what is the most efficient method to solve a given quadratic equation. If you think you have found a more efficient method than ours to solve a given quadratic equation, we invite you to post your equation and solution technique to the Forum or send us feedback through our Contact Form so we might compare your choice to ours. If we agree with you, we will gladly incorporate your thinking into our preliminary analysis.