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Find the monic quartic polynomial f(x) with rational coefficients whose roots include x = 2 - sqrt(2) and x = 3 + sqrt(6).

 Sep 18, 2020
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This will be \(f(x) = (x-2-\sqrt2)(x-2+\sqrt2)(x-3-\sqrt6)(x-3+\sqrt6)\)

 

I'll leave you to multiply it out to confirm that it does indeed have rational coefficients.

 

Edit:  corrected signs.  Thanks to EP for making me aware of this.

 Sep 18, 2020
edited by Alan  Sep 18, 2020

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