Algebra got you feeling Algeblah?
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The branch of mathematics known as algebra comes to us from the work of a medieval Persian scholar named Muhammad ibn Musa al-Kwarizmi, whose textbook on algebra was named Al-Kitab al-Jabr wa-l-Muqabala, meaning “The Compendium of Calculation by Completing and Balancing.” The short form of the title, al-Jabr, gave us the word algebra when it was rendered into Latin. Al-Kwarizmi shares the honor of fathering algebra with the ancient Greek mathematician Diophantus, who worked with equations involving variables.
At its heart, algebra is much as al-Kwarizmi described, a system for solving equations related to structure, relation, and quantity. Most students are familiar with elementary algebra, the type taught in high school. This type of algebra focuses on operations involving variables, including linear equations and quadratic equations. A linear equation is a mathematical expression which represents a straight line. The variables in a linear equation are all raised to the first power; that is, they are “just” variables, like this:
y = 3x + 7
By contrast, a quadratic equation is a “second order polynomial in a single variable” [1], a fancy way of saying that it contains only one type of variable, and that variable is raised to the second power, or squared, at least once in the equation, like this:
x2 + 15x + 56 = 0
Here there is only one variable, x, and at least one term in the polynomial is squared. The general form for any quadratic equation is
ax2 + bx + c = 0
By rewriting this equation via solving for x, we can produce a general formula that will show us the solution to any quadratic equation. This is the “quadratic formula” taught in most high school algebra courses:
x = -b ± √(b2-4ac)
2a
Using this formula with our example given above tells us that when x2 + 15x + 56 = 0, x = 8 and x = 7. There is another way to solve quadratic equations—factoring—that is a little more involved; but remembering the quadratic formula can serve as a handy way of solving equations when factoring is difficult or unclear.
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[1] “Quadratic Equation,” Wolfram Math World, 1999, <http://mathworld.wolfram.com/QuadraticEquation.html> (5 October 2006).
