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The equation whose roots are also the roots of the equation 1 - 3 1 1 6 4 1 3 x x 2 = 0 is

Options

  1. Ax 2 + x + 2 = 0
  2. Bx 2 + x − 2 = 0
  3. Cx 2 + 2 x + 2 = 0
  4. Dx 2 − x − 2 = 0

Correct answer

D. x 2 − x − 2 = 0

Step-by-step solution

Given equation is 1 - 3 1 1 6 4 1 3 x x 2 = 0 ⇒ 6 x 2 - 12 x + 3 x 2 - 4 + 3 x - 6 = 0 ⇒ 6 x 2 - 12 x + 3 x 2 - 12 + 3 x - 6 = 0 ⇒ 9 x 2 - 9 x - 18 = 0 ⇒ 9 x 2 - x - 2 = 0 Hence, the required equation is x 2 - x - 2 = 0

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