2 Solve a Quadratic Equation Using the Quadratic Formula Solve using the quadratic formula. a) 2x2 3x 1 0 b) 3n2 10n 8 0 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 19 (8) 4 Perform the operations. 3 117 4 9 (8) 9 8 17 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 3n2 10n 8 0 in the form ax2 bx c 0? Yes. Identify a, b, and c, and substitute them into the quadratic formula. a 3 b 10 c 8 n b 2b2 4ac 2a Quadratic formula n (10) 2(10)2 4(3)(8) 2(3) Substitute a 3, b 10, and c 8. n 10 1100 96 6 Perform the operations. n 10 14 6 Simplify the radicand. n 10 2 6 Simplify 14. Find the two values of n, one using the plus sign and the other using the minus sign: n 10 2 6 12 6 2 or n 10 2 6 8 6 4 3 Check the values in the original equation. The solution set is e 4 3 , 2 f . EXAMPLE 1 In-Class Example 1 Solve using the quadratic formula. a) 5h2 h 2 0 b) 2y2 5y 3 0 Answer: a) e1 141 10 , 1 141 10 f b) e 1, 3 2 f Are you writing out the steps as you read the example? YOU TRY 1 Solve using the quadratic formula. a) 5p2 p 3 0 b) 3r2 r 10 0 SECTION 10.3 www.mhhe.com/messersmith Solving Quadratic Equations Using the Quadratic Formula 623
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