2 Solve a Quadratic Equation Using the Quadratic Formula EXAMPLE 1 Solve using the quadratic formula. a) 2x2 3x 1 0 b) k2 10k 29 Solution a) Is 2x2 3x 1 0 in the form ax2 bx c 0? Yes. Identify the values of a, b, and c, and substitute them into the quadratic formula. a 2 b 3 c 1 x b 2b2 4ac 2a Quadratic formula (3) 2(3)2 4(2)(1) 2(2) Substitute a 2, b 3, and c 1. 3 29 (8) 4 Perform the operations. 3 117 4 The solution set is e3 117 4 , 3 117 4 f . This is the same result we obtained when we solved this equation by completing the square at the beginning of the section. b) Is k2 10k 29 in the form ax2 bx c 0? No. Begin by writing the equation in the correct form. k2 10k 29 0 Subtract 10k, and add 29 to both sides. a 1 b 10 c 29 Identify a, b, and c. k b 2b2 4ac 2a Quadratic formula (10) 2(10)2 4(1)(29) 2(1) Substitute a 1, b 10, and c 29. 10 2100 116 2 Perform the operations. 10 216 2 100 116 16 10 4i 2 116 4i 10 2 4 2 i 5 2i The solution set is {5 2i, 5 2i}. Write down the quadratic formula and the values of a, b, and c on your paper. YOU TRY 1 Solve using the quadratic formula. a) n2 9n 18 0 b) 5t2 t 2 0 626 CHAPTER 10 Quadratic Equations and Functions www.mhhe.com/messersmith
messersmith_power_intermediate_algebra_1e_ch4_7_10
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