In Section 7.5, we learned how to solve quadratic equations by factoring. For example, we can use the zero product rule to solve x2 3x 28 0. x2 3x 28 0 (x 7)(x 4) 0 Factor. b R x 7 0 or x 4 0 Set each factor equal to zero. x 7 or x 4 Solve. The solution set is {4, 7}. It is not easy to solve all quadratic equations by factoring, however. Therefore, we need to learn other methods for solving quadratic equations. In this chapter, we will discuss three more methods for solving quadratic equations. Let’s begin with the square root property. 1 Solve an Equation of the Form x2 k Look at the equation x2 4, for example. We can solve by factoring like this: x2 4 x2 4 0 Get all terms on the same side. (x 2)(x 2) 0 Factor. b R x 2 0 or x 2 0 Set each factor equal to zero. x 2 or x 2 Solve. giving us a solution set of {2, 2}. Or, we can solve an equation like x2 4 using the square root property, as we will see in Example 1a). Definition The Square Root Property Let k be a constant. If x2 k, then x 1k or x 1k. The solution is often written as x 1k, read as “x equals plus or minus the square root of k.” Note We can use the square root property to solve an equation containing a squared quantity and a constant. To do so, we will get the squared quantity containing the variable on one side of the equal sign and the constant on the other side. 606 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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