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Algebra 2

"I'm thinking of a number, and its name is `x' ..." So if

a x2 + b x + c = 0, (4.14)

what is x? Well, we can only say, "It depends." Namely, it depends on the values of a, b and c, whatever they are. Let's suppose the dimensions of all these "parameters" are mutually consistent4.7 so that the equation makes sense. Then "it can be shown" (a classic phrase if there ever was one!) that the "answer" is generally4.8

\begin{displaymath}x = {-b \pm \sqrt{b^2 - 4ac} \over 2a} .
\end{displaymath} (4.15)

This formula (and the preceding equation that defines what we mean by a, b and c) is known as the Quadratic Theorem, so called because it offers "the answer" to any quadratic equation (i.e. one containing powers of x up to and including x2). The power of such a general solution is prodigious. (Work out a few examples!) It also introduces an interesting new way of looking at the relationship between x and the parameters a, b and c that determine its value(s). Having x all by itself on one side of the equation and no x's anywhere on the other side is what we call a "solution" in Algebra. Let's make a simpler version of this sort of equation:

"I'm thinking of a number, and its name is `y' ..." So if y = x2, what is y? The answer is again, "It depends!" (In this case, upon the value of x.) And that leads us into a new subject....


next up previous
Next: Calculus Up: The Language of Math Previous: Trigonometry
Jess H. Brewer - Last modified: Fri Nov 13 16:19:29 PST 2015