What is the degree of the simplest polynomial with the zeroes:√2, 2√2 + i, and 2 + 2i ??
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My guess would be 6 since the simplest polynomial that I can come up with that has all of these as roots is (x² - 2)(x² - 4√2 x + 9)(x² - 4x + 8).
This means that , , are all factors of this polynomial. Therefore the simplest polynomial that has all these roots is :
Or, equivalently :
And the degree of this polynomial is, trivially, 3 (can be checked by expanding).
Originally Posted by VMM What is the degree of the simplest polynomial with the zeroes:√2, 2√2 + i, and 2 + 2i ?? Roots or zeros of polynomials of degree greater than 2 - Topics in precalculus
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