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

 

thank you!
 

 Feb 17, 2022
 #1
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There will be two more roots which are the conjugates of the given roots.

 

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

 

Can you do the expanding?

 Feb 18, 2022

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