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Find a monic quartic polynomial with rational coefficients whose roots include x = 1 - sqrt(2) and x = 2 + sqrt(7).

 Jun 26, 2021
 #1
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x =  1 + sqrt 2      and   2 - sqrt 7     are also  roots

 

We  have

 

(x - ( 1 + sqrt 2) ) ( x - (1 - sqrt 2)  )  ( x - ( 2 + sqrt 7))  ( x - (2 - sqrt 7))

 

Expanding  this we  get

 

x^4 - 6 x^3 + 4 x^2 + 10 x + 3

 

 

cool cool cool

 Jun 26, 2021

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