Quadratic (second-degree) equations are nice to work with because they’re manageable. Finding the solution or deciding whether a solution exists is relatively easy — easy, at least, in the world of mathematics. A quadratic equation is a quadratic expression with an equal sign attached.
As with linear equations, specific methods or processes, given in detail in this chapter, are employed to successfully solve quadratic equations. The most commonly used technique for solving these equations is factoring, but there’s also a quick-and-dirty rule for one of the special types of quadratic equations.
I have to warn you, though, that just because someone puts in some numbers and makes up a quadratic equation, that doesn’t mean there’s necessarily a solution or answer to it. (I show you how to tell if there’s no answer in this chapter.)
Quadratic equations are important to algebra and many other sciences. Some quadratic equations say that what goes up must come down. Other equations describe the paths that planets and comets take. In all, quadratic equations are fascinating — and just dandy to work with.
If the equation looks familiar, it means that you’ve read Chapter 9, which talks about factoring and working with quadratic expressions. Remember: An expression is comprised of one or more terms but has no equal sign. Adding an equal sign changes the whole picture: Now you have an equation that says something. The equation forms a true statement if the solutions are put in for the variables.