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

 Nov 19, 2021
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For a polynomial with rational coefficients, the the irrational roots come in pairs. 

If one root is 1 + sqrt(2), the other one must be 1 - sqrt(2). 

Similarly, if one root is 2 + sqrt(7), the other one must be 2 - sqrt(7). 

Now that the roots are found, you can find the factored form of the quartic. :))

 

=^._.^=

 Nov 19, 2021

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