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Mathematics
05.01.2022 00:23
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What is the degree of the simplest polynomial with integer coefficients that has

What is the degree of the simplest polynomial with integer coefficients that has โˆš2 , 2 , โˆš2 + i , and 2 + 2i as some of its zeros? a. 6
b. 7
c. 8
d. 9
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schnefai000
schnefai000
4,5(19 marks)

If the polynomial has integer coefficients, then any complex roots with non-zero imaginary part must occur along with their conjugates. If a + bi is a root, then so is a - bi.

The given polynomial would then have at least 6 roots: โˆš2, 2, โˆš2 + i and โˆš2 - i, and 2 + 2i and 2 - 2i. So the minimum degree is (A) 6.

savannahvargas512
savannahvargas512
4,9(33 marks)

B

Step-by-step explanation:

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