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neonofarm [45]
3 years ago
13

Find a cubic polynomial with integer coefficients that has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.

Mathematics
1 answer:
Paul [167]3 years ago
3 0

Find the powers a=\sqrt{2}+\sqrt{3}

$a^{2}=5+2 \sqrt{6}$

$a^{3}=11 \sqrt{2}+9 \sqrt{3}$

The cubic term gives us a clue, we can use a linear combination to eliminate the root 3 term $a^{3}-9 a=2 \sqrt{2}$ Square $\left(a^{3}-9 a\right)^{2}=8$ which gives one solution. Expand we have $a^{6}-18 a^{4}-81 a^{2}=8$ Hence the polynomial $x^{6}-18 x^{4}-81 x^{2}-8$ will have a as a solution.

Note this is not the simplest solution as $x^{6}-18 x^{4}-81 x^{2}-8=\left(x^{2}-8\right)\left(x^{4}-10 x^{2}+1\right)$

so fits with the other answers.

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Answer:

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3 years ago
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Evolutionary theories often emphasize that humans have adapted to their physical environment. One such theory hypothesizes that
timama [110]

Answer:

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Given that evolution theory hypothesizes that people should spontaneously follow a​ 24-hour cycle of sleeping and wakingdash–even if they are not exposed to the usual pattern of sunlight.

Sample size n = 8

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Since population std deviation is not known, and sample size is small we can use only t test

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24

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Answer:

B

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