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MHT CET20228 Aug 2022Evening ShiftMathematicsComplex NumberActual

If x=-2- 3 i , where i= -1 , then the value of 2 x^4+5 x^3+7 x^2-x+41 is

Options

  1. A6
  2. B-6
  3. C75
  4. D-76

Correct answer

A. 6

Step-by-step solution

aligned & x=-2+ 3 i & x+2=- 3 i & (x+2)^2=(- 3 i)^2 & x^2+4 x+4=-3 & x^2+4 x+7=0 & Now 2 x^4+5 x^3+7 x^2-x+41 & = (2 x^2-3 x+5 ) (x^2+4 x+7 )+6 & = (2 x^2-3 x+5 ) 0+6 & =6 aligned

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