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AP EAMCET202422 May 2024Morning ShiftMathematicsQuadratic EquationActual

If the number of real roots of x^9-x^5+x^4-1=0 is n , the number of complex roots having argument on imaginary axis is m and the number of complex roots having argument in 2^ nd quadrant is k , then m n k =

Options

  1. A6
  2. B9
  3. C12
  4. D24

Correct answer

A. 6

Step-by-step solution

aligned & x^9-x^5+x^4-1=0 (x^5+1 ) (x^4-1 )=0 & x^4=1 x=1,-1, i,-i & x^5=-1 x=-1, e^ - i 5 , e^ i 5 , e^ - 3 i 5 , e^ i 3 5 aligned No. of real roots is n=3, m=2, k=1 m n k=3 2 1=6

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