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AP EAMCET202022 Sep 2020Morning ShiftMathematicsQuadratic EquationActual

If " 2 i " is a root of f(z)=z^4+z^3+2 z^2+4 z-8=0 , then which among the following cannot be a root of f(z)=0 ?

Options

  1. A-2 i
  2. B1
  3. C–2
  4. D2

Correct answer

D. 2

Step-by-step solution

It is given that, f(z)=z^4+z^3+2 z^2+4 z-8 have a root 2 i , so one more root will be -2 i , so (z^2+4 ) is the factor of z^4+z^3+2 z^2+4 z-8 . So, z^4+z^3+2 z^2+4 z-8 = (z^2+4 ) (z^2+z-2 ) and z^2+z-2=(z+2)(z-1) Therefore, the roots of f(z) are 2 i,-2 i,-2 and 1 .

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