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# algebra 2 question. help is appreciated

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Find a monic quartic polynomial f(x) with rational coefficients whose roots include $$x=1-\sqrt2$$ and $$x=2+\sqrt5$$. Give your answer in expanded form.

thank you!

Feb 17, 2022

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There will be two more roots which are the conjugates of the given roots.

f(x)  =  [ x - (1 - sqrt(2) ] · [ x - (1 + sqrt(2) ] · [ x - (2 + sqrt(5) ] · [ x - (2 - sqrt(5) ]

Can you do the expanding?

Feb 18, 2022