alleryWhat must the degree of the minimal polynomial of a constructible number be?
AAlways exactly one
BA multiple of three
CAn odd prime number
DA power of two
Answer & Solution
Correct answer: D. A power of two
1. Each construction step solves at most a quadratic equation.
2. Repeated steps multiply the degree by two each time.
3. So the degree is a power of two, which rules out the cubic for cos 20 degrees.
_Source: Wikipedia, Angle trisection, section Proof of impossibility_
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