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# Polynomial

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

Jun 19, 2022

$$\text{The other two roots conjugates of the two given roots, then expand}$$ $$(x-r_1)(x-r_2)(x-r_3)(x-r_4)$$