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AP EAMCET2016MathematicsBinomial Theorem

To find the coefficient of x^4 in the expansion of 3 x (x-2)(x-1) , the interval in which the expansion isvalid, is

Options

  1. A-2 < x <
  2. B- 1 2 < x < 1 2
  3. C-1 < x < 1
  4. D- < x <

Correct answer

C. -1 < x < 1

Step-by-step solution

Given, 3 x (x-2)(x-1) can be written as 6 x-2 - 3 x-1 aligned & 3 x (x-2)(x-1) = 6 x-2 - 3 x-1 & =6(x-2)⁻¹-3(x-1)⁻¹ & =-3 (1- x 2 )+3(x-1)⁻¹ aligned It is valid iff | x 2 | < 1 and |x| < 1 aligned & |x| < 2 and |x| < 1 & x (-2,2) and x (-1,1) x (-1,1) aligned Hence, -1 < x < 1

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