Statement-1 If one root of \( A x^{3}+B x^{2}+C x+D=0 \) \( A \neq 0 \), is the arithmetic mean ...

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Statement-1 If one root of \( A x^{3}+B x^{2}+C x+D=0 \) \( A \neq 0 \), is the arithmetic mean of the other two roots, then the relation \( 2 B{ }^{3}+k_{1} A B C+k_{2} A^{2} D=0 \) holds good and then \( \left(k_{2}-k_{1}\right) \) is a perfect square.
Statement-2 If \( a, b, c \) are in AP, then \( b \) is the arithmetic mean of \( a \) and \( c \).
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