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If the graph of the function y = a - b 2 x 2 + 2 a + b - 2 c x + 1   ∀ a ≠ b is strictly above the x -axis, then

Options

  1. Aa < b < c
  2. Ba < c < b
  3. Cb < a < c
  4. Dc < b < a

Correct answer

B. a < c < b

Step-by-step solution

D = B 2 - 4 A C = 2 a + b - 2 c 2 - 4 a - b 2 = 4 a + b - 2 c 2 - a - b 2 = 4 a + b - 2 c - a + b a + b - 2 c + a - b = 4 2 b - 2 c 2 a - 2 c = 16 b - c a - c = 16 c - b c - a If c lies between a and b , then D is negative. Hence, the roots will be imaginary and the graph will be entirely above the x -axis as the coefficient of x 2 is positive.

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