Technical Mathematics, Sixth Edition

Chapter 12. Quadratic Equations

OBJECTIVES When you have completed this chapter you should be able to Solve quadratics using a calculator's equation solver. Solve quadratics using a calculator that can do symbolic algebra. Solve quadratics by graphing, either manually or by calculator. Solve quadratics by the quadratic formula. Apply quadratics to a variety of applications.

So far we have only solved first-degree (linear) equations, as well as sets of linear equations. Now we move on to equations of second degree, or quadratic equations.

We have already solved equations using calculators that have a built-in equation solver, and using calculators that can do symbolic processing. Also, in our chapter on graphing, we learned how to graphically find the approximate solution to any equation. We will start by applying those methods to quadratic equations. The methods are no different here, except we must look for two solutions instead of one. We will also show the more traditional manual method, the use of the quadratic formula.

As usual, we will follow the mathematics with numerous applications. Take, for example, a simple falling-body problem, Fig. 12-1: "If an object is thrown downward with a speed of 15.5 ft/s, how long will it take to fall 125 ft?" If we substitute s = 125 ft, v₀ = 15.5 ft/s, and a = 32.2 ft/s² into the equation for a freely falling body

we get

125 = 15.5t + 16.1 ...