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Find the monic polynomial f(x) of minimal degree such that f(1 + i) = f(−1 + i) = 0 and all the coefficients of f(x) are real.

 Mar 13, 2021
 #1
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The roots you specfy  will not produce a polynomial  with real coefficients

 

I think  you must  mean that    f( 1 + i)    = f( 1 - i)  =  0 

 

So we  have

 

f(x)  =  (x - ( 1 + i) )   (x - ( 1 - i ) )   =

 

(x - 1   - i )   (  x - 1  + i)    =

 

x^2  -x  - ix  - x + 1  + i   + ix - i  - i^2   =

 

x^2  - 2x  + 2

 

 

cool cool cool

 Mar 13, 2021

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