Unformatted text preview: MAC1105: Quiz #10 Solutions
July 14, 2010 In the topright corner of a clean sheet of paper, write your name, UFID, and section number. Please use a pen with blue or black ink. When you are nished, FOLD your paper in half lengthwise and write your name on the back. 1. Solve the following quadratic equations by factoring: (a) x2 = 3x + 4
x2  3x  4 = 0 (x  4)(x + 1) = 0 x = 4; x = 1 (b) 4x2 + 5x = 6 4x2 + 5x  6 = 0. Now use the AC method: 6 4 = 24, 3 + 8 = 5, so write (4x2  3x) + (8x  6) = 0 x(4x  3) + 2(4x  3) = 0 3 (x + 2)(4x  3) = 0 x = 2; x = 4 . 2. Solve the following quadratic equations using the squareroot property: (a) 2x2 + 72 = 0 2x2 = 72 x2 = 36 x = 36 x = 6i. (x  1)2 = 4 x  1 = 2 x = 1 2 x = 3; x = 1. (b) (x  1)2  4 = 0 3. Solve the following quadratic equation by completing the square: (a) x2  4x = 7 Here, a = 1 and the constant term is already on the righthand side, so all we need to do is transform the lefthand side into a perfect square trinomial:
x2  4x + 4 = 7 + 4 (x  2)2 = 11 x  2 = 11 x = 2 11 1 ...
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 Summer '10
 Picklesimer
 Algebra, Quadratic equation, Elementary algebra, following quadratic equations

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