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# Help!

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Find a monic polynomial of degree 4, in x, with rational coefficients such that $$\sqrt{2} +\sqrt{3}$$ is a root of the polynomial.

May 28, 2019

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$$\text{based on the problem last night I can write this out right off}\\ p(x) = (x-\sqrt{2}-\sqrt{3})(x-\sqrt{2}+\sqrt{3})(x+\sqrt{2}-\sqrt{3})(x+\sqrt{2}+\sqrt{3})\\~\\ p(x) = x^4-10 x^2+1$$

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May 28, 2019

$$\text{based on the problem last night I can write this out right off}\\ p(x) = (x-\sqrt{2}-\sqrt{3})(x-\sqrt{2}+\sqrt{3})(x+\sqrt{2}-\sqrt{3})(x+\sqrt{2}+\sqrt{3})\\~\\ p(x) = x^4-10 x^2+1$$