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AP EAMCET202023 Sep 2020Morning ShiftMathematicsQuadratic EquationActual

Which of the following is not a root of f ( x ) = x 3 - 11 x 2 + 36 x - 36 ?

Options

  1. A2
  2. B4
  3. C3
  4. D6

Correct answer

B. 4

Step-by-step solution

The following is not a root of x 3 - 11 x 2 + 36 x - 36 = 0 ⇒ x 3 - 2 x 2 - 9 x 2 + 18 x + 18 x - 36 = 0 ⇒ x 2 ( x - 2 ) - 9 x ( x - 2 ) + 18 ( x - 2 ) = 0 ⇒ ( x - 2 ) ( x 2 - 9 x + 18 ) = 0 ⇒ x = 2 ,       x = 9 ± 81 - 72 2 ⇒ x = 2 ,   x = 9 ± 3 2 ⇒ x = 2 ,   x = 6 , 3 ⇒ x = 2 , 3 , 6   are roots ⇒ x = 4   is not a root.

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