Use your chart to help you decide which method to use to solve a quadratic equation. d) Which method should we use to solve (5n 3)2 12 0? We could square the binomial, combine like terms, then solve, possibly, by factoring or using the quadratic formula. However, this would be very ineffi cient. The equation contains a squared quantity and a constant. We will solve (5n 3)2 12 0 using the square root property. (5n 3)2 12 0 (5n 3)2 12 Add 12 to each side. 5n 3 112 Square root property 5n 3 213 Simplify 112. 5n 3 213 Add 3 to each side. 3 213 n 5 Divide by 5. The solution set is e3 213 5 , 3 213 5 f . YOU TRY 1 Solve. a) 3t2 2 8t b) m2 36 13m c) (4r 1)2 10 0 d) w2 8w 2 0 ANSWERS TO YOU TRY EXERCISE 1) a) e4 122 3 , 4 122 3 Objective 1: Decide Which Method to Use to Solve a Quadratic Equation Keep in mind the four methods we have learned for solving quadratic equations: factoring, the square root property, completing the square, and the quadratic formula. Solve the equations using one of these methods. 1) f 2 75 0 2) t2 8t 4 3) a(a 1) 20 {5, 4} 4) 3m2 7 4m 5) v2 6v 7 0 6) 4u2 5u 6 0 7) 3x(x 3) 5(x 1) 8) 5 ( p 4)2 7 9) n2 12n 42 0 10) {513, 513} {4 215, 4 215} {3 12, 3 12} e 1 2 r2 3 4 3 2 r 11) 12 (2k 1)2 3 12) h2 7h 15 0 3 4 , 2 f e5, 1 3 f e3 115 2 , 3 115 2 f f b) {4, 9} c) d) {4 312, 4 312} 13) 1 x2 40 3x 20 {4, 10} 14) 72 2p2 {6, 6} 15) b2 6b 5 16) 3m3 42m 27m2 17) q(q 12) 3(q2 5) q {3 114, 3 114} {7, 2, 0} e 5 2 18) w2 3w {0, 3} 19) , 3 f 9 c 1 18 c2 {3, 6} e3 1105 3 1105 20) 2t(2t 4) 5t 6 8 21) (3v 4)(v 2) 9 22) y2 4y 2 23) 2r2 3r 2 0 24) (6r 1)(r 4) 2(12r 1) 25) 5m m2 {0, 5} 26) 6z2 12z 18 0 27) 4m3 9m 28) , 8 x2 1 4 8 1 x {8, 4} 29) 2k2 3 9k 30) 6v2 3 15v f {2 16, 2 16} e2, 1 2 f e 2 3 , 1 2 f e 3 2 , 0, 3 2 f e 9 157 4 , 9 157 4 f e 5 117 4 , 5 117 4 f Putting It All Together Exercises Do the exercises, and check your work. *Additional answers can be found in the Answers to Exercises appendix. 630 CHAPTER 10 Quadratic Equations www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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