If the roots of the equation $(b c)x^2 + (c a)x + (a b) = 0$ are equal, then $a, 2b, c$ will be in.

For the equation to have equal roots, its discriminant must equal zero, so we set (ca)^2 - 4(bc)(ab) = 0. This simplifies to c^2 times a^2 = 4 times a times b squared times c. Assuming a, b, and c are non-zero and dividing by ac gives ac = 4b^2, which can be rewritten as b^2 = ac. Since the square of the middle term equals the product of the first and third terms, a, 2b, and c are in geometric progression.

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