Multiple choice

If $a, b, c$ are in AP and if quadratic equations $(b - c)x^2 + (c - a)x + (a - b) = 0, 2(c + a)x = 0$ have a common root, then

  1. $a^2, b^2, c^2$ are in AP
  2. $a^2, c^2, b^2$ are in AP
  3. $a^2, c^2, b^2$ are in GP

  4. None of these
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A Correct answer
Explanation

If a, b, c are in AP, then 2b = a + c. The common root condition leads to the relation that the coefficients satisfy a specific property, which simplifies to showing that a^2, b^2, c^2 are in AP when specific conditions are met.

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