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Quiz10solutions

# Quiz10solutions - MAC1105 Quiz#10 Solutions In the...

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Unformatted text preview: MAC1105: Quiz #10 Solutions July 14, 2010 In the top-right 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 square-root 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 right-hand side, so all we need to do is transform the left-hand 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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