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BITSAT2012MathematicsComplex NumberActual

If x= - ²-2, then the value of x⁴+3 x³+2 x²-11 x-6 is

Options

  1. A1
  2. B-1
  3. C2
  4. DNone of these

Correct answer

A. 1

Step-by-step solution

We have, x= - ²-2 or x+2= - ² Squaring, x²+4 x+4= ²+ ⁴-2 ³= ²+ ³ -2 ³= ²+ -2 [ ³=1 ]=-1-2=-3 ²+4 x+7=0 Dividing x⁴+3 x³+2 x²-11 x-6 by x²+4 x+7 we get x⁴+3 x³+2 x²-11 x-6= (x²+4 x+7 ) (x²-x-1 )+1=(0) ( x ²- x -1 )+1=0+1=1

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