MAT

# 10 20 8 6 using the formula the quadratic formula

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10 20 8 6 Using the Formula The quadratic formula solves any quadratic equation. Simply identify a , b , and c and insert those numbers into the formula. Note that if b is positive then b (the opposite of b ) is a negative number. If b is negative, then b is a positive number. dug22241_ch10a.qxd 11/10/2004 18:30 Page 631

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Because the solutions to the equations in Examples 1 and 2 were rational num- bers, these equations could have been solved by factoring. In Example 3 the solutions are irrational. 632 Chapter 10 Quadratic Equations and Inequalities 10-16 In this form we get a 4, b 12, and c 9. x Because b 12, b 12. 12 1 8 44 144 12 8 0 1 8 2 3 2 Check 3 2 in the original equation. The solution set is 3 2 . Now do Exercises 13–18 12 ( 12) 2 4(4)(9) 2(4) Calculator Close-Up Note that the single solution to 4 x 2 12 x 9 0 corresponds to the single x -intercept for the graph of y 4 x 2 12 x 9. 10 2 2 4 E X A M P L E 3 Two irrational solutions Solve 2 x 2 6 x 3 0. Solution Let a 2, b 6, and c 3 in the quadratic formula: x 6 4 36 24 6 4 12 6 4 2 3 2 ( 3 2 2 3 ) 3 2 3 Check these values in the original equation. The solution set is 3 2 3 . Now do Exercises 19–24 6 (6) 2 4(2)(3) 2(2) Calculator Close-Up The two irrational solutions to 2 x 2 6 x 3 0 correspond to the two x -intercepts for the graph of y 2 x 2 6 x 3. 5 3 5 5 dug22241_ch10a.qxd 11/10/2004 18:30 Page 632

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