Homework 1 - MATH 74 HOMEWORK 1: DUE WEDNESDAY 9/5 Let us...

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Unformatted text preview: MATH 74 HOMEWORK 1: DUE WEDNESDAY 9/5 Let us take for granted the following proposition. Proposition. For any real numbers a, b, c , we have • If b 2- 4 ac > , then there are exactly two real numbers t with the property that at 2 + bt + c = 0 , namely, the numbers- b ± √ b 2- 4 ac 2 a . • If b 2- 4 ac = 0 , then there is exactly one real number t with the property that at 2 + bt + c = 0 , namely t =- b 2 a . • If b 2- 4 ac < , then there are no real numbers t satisfying at 2 + bt + c = 0 . (You may assume the arithmetic of real numbers is understood, and that square roots of positive real numbers are understood and behave the way you know they do from high school.) 1(a). Find all real numbers x satisfying x 4- 6 x 2 +7 = 0. Write it up in any format that makes clear what you did. 1(b). Find all real numbers x satisfying x 4- 2 x 2- 1 = 0. 2. Let x denote the weight of an elephant, and y the weight of a mosquito. Denote the sum of their weights by 2 v , so that x + y = 2 v . From x + y = 2 v we can conclude both (1) x- 2 v...
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This note was uploaded on 02/10/2010 for the course MATH 74 taught by Professor Courtney during the Fall '07 term at University of California, Berkeley.

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Homework 1 - MATH 74 HOMEWORK 1: DUE WEDNESDAY 9/5 Let us...

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