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# Polynomials and coefficients

1. Find a minimal degree polynomial $$p(x)$$ with integer coefficients for which $$a = \sqrt2 + \sqrt[3]{2}$$ is a root.

2. Suppose $$p(x)$$ is a polynomial with integer coefficients, show that if $$p(a) = 1$$ for some integer $$a$$, then $$p(x)$$ has at most two integer roots.

Note by Lupa Green
1 year, 10 months ago

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What have you tried? What have you found out?

Staff - 1 year, 10 months ago