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Manipal MET2013MathematicsDeterminants

Coefficient of x in f(x)= | array ccc x & (1+ x)^3 & x 1 & (1+x) & 2 x^2 & (1+x)^2 & 0 array | is

Options

  1. A0
  2. B1
  3. C-2
  4. DCannot be determined

Correct answer

C. -2

Step-by-step solution

Coefficient x in f(x) is equal to coefficient of x in | array ccc x & (1+x- x^3 3! )^3 & 1- x^2 2! 1 & x- x^2 2 & 2 x^2 & 1+x^2 & 0 array |= coefficient of x in | array ccc x & 1 & 1 1 & x & 2 x^2 & 1 & 0 array | aligned & = Coefficient of x in [x(0-2)-1 (0-2 x^2 ) . & .+1 (1-x^3 ) ] aligned =-2

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