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KVPY2019MathematicsDeterminants

The number of integers x satisfying - 3 x 4 + det 1 x x 2 1 x 2 x 4 1 x 3 x 6 = 0 is equal to

Options

  1. A1
  2. B2
  3. C5
  4. D8

Correct answer

B. 2

Step-by-step solution

Given, - 3 x 4 + det 1 x x 2 1 x 2 x 4 1 x 3 x 6 = 0 ⇒   x 8 + x 5 + x 5 - x 4 - x 7 - x 7 = 3 x 4 ⇒   x 8 - 2 x 7 + 2 x 5 - 4 x 4 = 0 ⇒   x 4 x 4 - 2 x 3 + 2 x - 4 = 0 ⇒   x 4 x 3 x - 2 + 2 x - 2 = 0 ⇒   x 4 x 3 + 2 x - 2 = 0 ∵ x is an integer, so x = 0 ,   2 .

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