Let 1,ω,ω2 be the cube roots of unity. The least possible degree of a polynomial with real coefficients, having 2ω,2+3ω,2+3ω2 and 2–ω–ω2 as roots is
A
8
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B
5
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C
6
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D
4
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Solution
The correct option is B5 Roots are 2ω,2+3ω,2+3ω2,2–ω–ω2.
i.e. 2ω,2+3ω,2+3ω2,3
The roots 2+3ω,2+3ω2 can come from a 2nd degree polynomial with real coefficients.
Again the root 2ω can come from a 2nd degree polynomial with real coefficients.
The root 3 comes from a linear polynomial.
Thus the least possible degree is 5.