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Consider the cubic f x = x 3 - 3 x + a , where a ∈ 0 , 2 . Then, the equation f x = 0 has

Options

  1. A3 real solutions
  2. B2 real solutions
  3. C1 real solution
  4. Dno real solutions

Correct answer

A. 3 real solutions

Step-by-step solution

f ′ x = 3 x 2 − 3 = 3 x - 1 x + 1 Also, f - 1 = a + 2 > 0 f 1 = a - 2 < 0 Hence, f x = 0 has 3 real solutions.

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