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AP EAMCET202021 Sep 2020Morning ShiftMathematicsComplex NumberActual

If ((2+i) ) is a root of the equation (x^3-5 x^2+9 x-5=0 ), then the other roots are

Options

  1. A1 and ((2-i) )
  2. B-1 and ((3+i) )
  3. C0 and 1
  4. D-1 and ((-2+i) )

Correct answer

A. 1 and ((2-i) )

Step-by-step solution

It is given that (2+i ) is the root of the equation (x^3-5 x^2+9 x-5=0 ), so another non-real complex root will be (2-i ). Now, let the third root is ( ), so by product of roots, we have ((2+i)(2-i) =5 =1 ) Hence, option (a) is correct.

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