ProblemSet2 Solutions

ProblemSet2 Solutions - Department of Economics Ryerson...

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Department of Economics Ryerson University ECN230-Mathematics For Economics Problem Set #2 - Solutions EXERCISE 3.3 Problem 3: (a) Cubic Equation: ( x x 1 )( x x 2 x x 3 )=0 ( x 6) ( x +1)( x 3) = 0 ¡ x 2 5 x 6 ¢ ( x 3) = 0 x 3 8 x 2 +9 x +18=0. (b) Quartic Equation: ( x x 1 x x 2 x x 3 x x 4 ( x 1) ( x 2) ( x 3) ( x 5) = 0 ¡ x 2 3 x +2 ¢ ( x 3) ( x 5) = 0 ¡ x 3 6 x 2 +11 x 6 ¢ ( x 5) = 0 x 4 11 x 3 +41 x 2 61 x +30=0. Problem 4: (a) x =1isaroot: 1+( 2)+3+( 2) = 0. (b) x =1isnotaroot: 2+( 1 2 )+1+( 2) = 1 2 6 =0. (c) x =1isaroot: 3+( 1)+2+( 4) = 0. Problem 5: (a) Divisors of a 0 =6: r = { 1 , 1 , 2 , 2 , 3 , 3 , 6 , 6 } Divisors of a 3 =1: s = { 1 , 1 } 1
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Possible rational roots: r s = { 1 , 1 , 2 , 2 , 3 , 3 , 6 , 6 } Roots: x 1 = 1 ,x 2 =2 3 =3 (b) Divisors of a 0 = 1: r = { 1 , 1 } Divisors of a 3 =8: s = { 1 , 1 , 2 , 2 , 4 , 4 , 8 , 8 } Possible rational roots: r s = © 1 , 1 , 1 2 , 1 2 , 1 4 , 1 4 , 1 8 , 1 8 ª Roots: x 1 = 1 2 = 1 2 3 = 1 4 (c) Multiplying both sides by 8 yields: 8 x 3 +6 x 2 3 x 1=0. The resulting equation is the same as the one in part (b) above. (d) [Note: There is a typo in the textbook regarding the sign of the coe cient of x . It should be + 3 2 instead of 3 2 .] Multiplying both sides by 4 yields: 4 x 4 24 x 3 +31 x 2 x 8=0.
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This homework help was uploaded on 04/18/2008 for the course ECONOMICS ECN 230 taught by Professor Angrydis during the Winter '08 term at Ryerson.

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ProblemSet2 Solutions - Department of Economics Ryerson...

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