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Let and be the roots of the equation px^2 + qx + r = 0, p 0. If p, q, r are in A.P. and 1/ + 1/ = 4, then the value of | - | is

1. 34/9
2. 213/9
3. 61/9
4. 217/9

Correct answer: 213/9

Solution

The roots of the quadratic equation can be expressed in terms of the coefficients using Vieta's formulas. Given that p, q, and r are in arithmetic progression, we can derive relationships between the roots and the coefficients, leading to the conclusion that the absolute difference between the roots is 2√13/9.

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