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BITSAT2024MathematicsDeterminantsActual

If x is a complex root of the equation | array ccc 1 & x & x x & 1 & x x & x & 1 array |+ | array ccc 1-x & 1 & 1 1 & 1-x & 1 1 & 1 & 1-x array |=0 , then x²⁰⁰⁷+x⁻²⁰⁰⁷=

Options

  1. A1
  2. B-1
  3. C-2
  4. D2

Correct answer

C. -2

Step-by-step solution

Expanding the two determinants, we get (1-3 x^2+2 x^3 )+ (3 x^2-x^3 )=0 x^3+1=0 x=- ,- ^2,-1x²⁰⁰⁷+x⁻²⁰⁰⁷=-1-1=-2

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