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BITSAT2019MathematicsQuadratic EquationActual

Let p and q be roots of the equation x 2 - 2 x + A = 0 and let r and s be the roots of the equation x 2 - 18 x + B = 0 . If p < q < r < s are in arithmetic progression, then A and B are

Options

  1. A- 3 , - 77
  2. B3 , - 77
  3. C- 3 , 77
  4. D3 , 77

Correct answer

C. - 3 , 77

Step-by-step solution

x 2 - 2 x + A = 0 ⇒   x = 1 ± 1 - A ∴   p = 1 - 1 - A , q = 1 + 1 - A Similarly, r = 9 - 81 - B , s = 9 + 81 - B p , q , r , s are in AP . ∵   q - p = s - r ⇒   2 1 - A = 2 81 - B ⇒   B = 80 + A and q - p = r - q ⇒   3 1 - A = 8 - 81 - B ⇒   A = - 3 , B = 77

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