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AP EAMCET202119 Aug 2021Evening ShiftMathematicsQuadratic 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 A P , 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

Let the four numbers in A . P . be p = a - 3 d ,   q = a - d ,   r = a + d ,   s = a + 3 d . Now, p and q are the roots of the quadratic equation x 2 - 2 x + A = 0 . Therefore, using the sum and product of roots of a quadratic equation, we get p + q = 2       … i p q = A       … i i And, r , s are the roots of the quadratic equation x 2 - 18 x + B = 0 . Therefore, r + s = 18       … i i i r s = B       … i v By i and

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