+0  
 
0
98
1
avatar

Find a monic quartic polynomial f(x) with rational coefficients whose roots include 1 - sqrt2  and 2 + sqrt5 . Give your answer in expanded form.

 May 22, 2020
 #1
avatar+21953 
0

The four roots of this quartic are:  1 - sqrt(2)   1 + sqrt(2)   2 + sqrt(5)   2 - sqrt(5)

 

The polynomial will be: 

  [ x - ( 1 - sqrt(2) ) ] · [ x - ( 1 + sqrt(2) ) ] · [ x -  ( 2 + sqrt(5) ] · [ x - ( 2 - sqrt(5) ) ]  =  0

 

You'll need to multiply it out ...

 May 22, 2020

9 Online Users

avatar
avatar
avatar