UPSC NDA II 2023 Mathematics Solved Paper

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Consider the following for the next three (03) items that follow :
Consider equation-I : z3+2z2+2z+1=0 and equation-II : z1985+z100+1=0.
[NDA II 2023]
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What is the number of common roots of equation-I and equation-II ?
[NDA II 2023]
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