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Quiz11solutions

Quiz11solutions - MAC1105 Quiz#11 Solutions In the...

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Unformatted text preview: MAC1105: Quiz #11 Solutions July 18, 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. State the quadratic formula: 2. Solve the following (a) x= -b b2 - 4ac 2a using the quadratic formula: -(-5) (-5)2 - 4(3)(7) 5 = 2(3) 5 59i 25 - 84 = 6 6 3x2 - 5x + 7 = 0 a = 3; b = -5, c = 7 x = (b) 4x2 + 3x + 2 = 0 a = 4; b = 3; c = 2 x = -3 32 - 4(4)(2) -3 9 - 32 -3 i 23 = = 2(4) 8 8 3. The product of a positive number, and 3 less than 2 times the number is 54. Find the two numbers. (Hint: Call the number The product, which in 441 = 21) x, so that 3 less than 2 times the number will be 2x - 3. x(2x - 3) is given to be 54, so we can write x(2x - 3) = 54, 2 standard form gives 2x - 3x - 54 = 0. This can be solved a = 2, b = -3, and with either factoring or the quadratic formula, here we use the quadratic formula with c = -54: 9 + 432 3 21 = 4 4 x= So -(-3) (-3)2 - 4(2)(-54) 3 = 2(2) -18 4 . Since we are told that the number is positive, we want the solution x = 6. The other number is then 2(6) - 3 = 9. x=6 or x= 1 ...
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