Assignment 7 Solutions

Assignment 7 Solutions - Assignment 7 1 What are the...

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Assignment 7: 1. What are the solutions to this set of equations: x + y = 5 xy = - 36 ( x, y ) = (9 , - 4) or ( x, y ) = ( - 4 , 9) 2. Given the polynomial x 2 + ax + b , what is ( r 1 + r 2 ) 2 a 2 (this question was supposed to be expand r 2 1 + r 2 2 ) 3. What number will always divide 4 n - 1? 4 n - 1 n = (4 - 1)(4 n - 1 - 4 n - 2 · · · - 4 + 1 This is divisible by 4 - 1 = 3. 4. How many real roots does x 5 - x have? The 3 real roots are: x = 1 , 0 , - 1. x = i, - i are not real. 5. What is the formula for 1 + x + x 2 + ... + x n - 1 ? (Try putting in a = 1, b = x ) (1 - x n ) = (1 - x )(1 + x + x 2 + ... + x n - 1 ) So the formula is 1 - x n 1 - x . 6. Does the last formula work for x = 1? If so, find the value for n = 15. If not, use the formula with x = - 1 for n = 14. The formula doesnt work for x=1. For n = 14, the formula gives: 1 - ( - 1) 14 1 - ( - 1) = 0 / 2 = 0 7. What are the solutions to this set of equations: x + y + z = 2 xy + xz
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