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AP EAMCET20225 Jul 2022Evening ShiftMathematicsComplex NumberActual

If x=-5+2 -4 , then the value of x^4+9 x^3+35 x^2-x+4 is

Options

  1. A80
  2. B160
  3. C-160
  4. D-80

Correct answer

C. -160

Step-by-step solution

x=-5+2 -4 aligned & x+5=4 i & (x+5)^2=(4 i)^2 & x^2+10 x+25=-16 & x^2+10 x+41=0 aligned Let x^4+9 x^3+35 x^2-x+4= (x^2+10 x+41 )(p(x))+ R aligned & x^2+10 x+41=0 & x^2+9 x^3+35 x^2-x+4= R aligned i.e. Remainder when x^4+9 x^3+35 x^2-x+4 is divided by x^2+10 x+41 R=-160x^4+9 x^3+35 x^2-x+4=-160

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