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Andrew made an error in determining the polynomial equation of smallest degree whose roots are 3, 2+2i and 2-2i. 

 

- Review Andrews work, identify the error and correct all the work from that point forward that is affected by this error. 

- Include at least one sentence explaining his error. use mathematical vocabulary

 

(x-3)(x+2+2i)(x+2-2i)=0

(x-3)(x^2+4x+8)=0

x^3+x^2-4x-24=0

 

Hello, thank you for reading :) Would you please help me on this

 Aug 15, 2023
 #1
avatar+129657 
+1

(x -3)  ( [ x - (2+2i) ]  [ x - (2 - 2i)]   = 0

 

(x - 3)  [  x^2  - (2 - 2i)x - (2 + 2i)x + (2 + 2i) ( 2 -2i)  ]  =  0

 

(x - 3) [ x^2 - 4x + 4 - 4i^2 ]  =  0             [ i^2  = -1 ]

 

(x - 3) [ x^2 - 4x + 8]  =  0         The error occurs in the  second  step [ -4x instead of 4x ]

 

x^3 - 4x^2 + 8x  - 3x^3 + 12x - 24 = 0

 

x^3 - 7x^2 + 20x - 24 = 0

 

 

cool cool cool

 Aug 15, 2023
 #2
avatar+124 
0

Okay, thank you so much CPhill :))

thebestchesscat  Aug 15, 2023

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