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
- A- 3 , - 77
- B3 , - 77
- C- 3 , 77
- 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