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Find a monic quartic polynomial f(x) with rational coefficients whose roots include 1 - sqrt(3) and 2 + sqrt(3). Give your answer in expanded form.

 Dec 16, 2021
 #1
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If  1 - sqrt(3)  is a solution,  1 + sqrt(3)  will also be a solution.

If  2 + sqrt(3)  is a solution,  2 - sqrt(3)  will also be a solution.

 

The polynomial, in factored form is:  [ x - (1 - sqrt(3)) ] · [ x - (1 + sqrt(3)) ] · [ x - (2 + sqrt(3) ] · [ x - (2 - sqrt(3) ]  =  0

 

Expand this expression for your answer.

 Dec 16, 2021

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