If the sum of the roots of the quadratic equation ax^2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then a/c, b/a and c/b are in
- A. arithmetic progression
- B. geometric progression
- C. arithmetic-geometric-progression
- D. harmonic progression
Answer: D. harmonic progression
Explanation: For ax² + bx + c = 0, α+β = −b/a and αβ = c/a. Sum of squares of reciprocals: 1/α² + 1/β² = (b²−2ac)/c². Equating to α+β gives −b/a = b²/c² − 2a/c ⇒ 2a/c = b²/c² + b/a. Simplifying shows c/a, a/b, b/c are in AP, so their reciprocals a/c, b/a, c/b are in harmonic progression (HP).