Find a monic quartic polynomial, in $x,$ with rational coefficients such that $2+\sqrt{2}$ and $1-\sqrt{3}$ are roots of the polynomial.
Question:
Find a monic quartic polynomial, in $x,$ with rational coefficients such that $2+\sqrt{2}$ and $1-\sqrt{3}$ are roots of the polynomial.
Answer:
Let's think step by step.

user
x^4-6x^3+8x^2+4x-4
Find a monic quartic polynomial, in $x,$ with rational coefficients such that $2+\sqrt{2}$ and $1-\sqrt{3}$ are roots of the polynomial.
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