Paragraph Roots of z^n-1=0 are 1, , ^2, ^3, . . ^ n-1 where = 2 n +i 2 n so z^n-1=(z-1)(z- ) ( z - ^ n -1 ) On the basis of above information, answer the following questions : Question If n =7 , then the equation whose roots are + ^2+ ^4 an

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Paragraph Roots of z^n-1=0 are 1, , ^2, ^3, . . ^ n-1 where = 2 n +i 2 n so z^n-1=(z-1)(z- ) ( z - ^ n -1 ) On the basis of above information, answer the following questions : Question If n =7 , then the equation whose roots are + ^2+ ^4 and ^3+ ^5+ ^6 is -

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Correct answer: D. x^2+x+2=0

n =7, ^7=1 and 1+ + ^2+ . . ^6=0 Sum of the roots = + ^2+ ^4+ ^3+ ^5+ ^6=-1 Product of the roots = ( + ^2+ ^4 ) ( ^3+ ^5+ ^6 )= ^4+ ^6+ ^7+ ^5+ ^7+ ^8+ ^7+ ^9+ ¹⁰=2+ (1+ + ^2+ ^3+ ^4+ ^5+ ^6 )=2 So the required equation is x^2-(-1) x+2=0 x^2+x+2=0

Paragraph Roots of z^n-1=0 are 1, , ^2, ^3, . . ^ n-1 where = 2 n +i 2 n so z^n-1=(z-1)(z- ) ( z - ^ n -1 ) On the basis of above information, answer the following questions : Question If n =7 , then the equation whose roots are + ^2+ ^4 and ^3+ ^5+ ^6 is -

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