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If a > 2 , then the roots of the equation 2 - a x 2 + 3 a x - 1 = 0 are

Options

  1. Aone positive and one negative
  2. Bboth negative
  3. Cboth positive
  4. Dboth imaginary

Correct answer

C. both positive

Step-by-step solution

Let, f x = x 2 - 3 a a - 2 x + 1 a - 2 = 0 D = 9 a 2 a - 2 2 - 4 1 a - 2 = 9 a 2 - 4 a + 8 a - 2 2 = 8 a 2 + a - 2 2 + 4 a - 2 2 > 0 f 0 = 1 a - 2 > 0 and - B 2 A = 3 a 2 a - 2 > 0 Since, D > 0 , f 0 > 0 , - B 2 A > 0 Hence, both roots of the given equation are positive.

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