Quadratic Equations Sequences Series

Let a and b be roots of the equation px2 + qx + r, p ≠ 0. If p, q, r are in A.P. and 1/a + 1/b = 4, then the value of |a - b| is

  1. 2√17 / 9
  2. √61 / 9
  3. √34 / 9
  4. 2√13 / 9

Solution

1/a + 1/b = 4

2q = p + r

-2(a + b) = 1 + ab

-2(1/a + 1/b) = 1/ab +1

1/ab = -9

Equation having roots a,b is 9x2 + 4x - 1 = 0

a,b = -4 ± √(16 + 36) / 18

The correct option is D.